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Fermi–Dirac statistics
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In quantum statistics, a branch of physics, Fermi–Dirac statistics describes a distribution of particles over energy states in systems consisting of manyPaul Dirac (5,922 words) [view diff] no match in snippet view article find links to article

"Dirac" redirects here. For other uses, see Dirac (disambiguation). Paul Adrien Maurice Dirac OM FRS (/dɪˈræk/ di-RAK; 8 August 1902 – 20 October 1984)Dirac Prize (815 words) [view diff] no match in snippet view article find links to article

The Dirac Prize is the name of four prominent awards in the field of theoretical physics, computational chemistry, and mathematics, awarded by differentDirac (video compression format) (1,378 words) [view diff] no match in snippet view article

dirac-research (formerly just called "Dirac") are open and royalty-free software implementations (video codecs) of Dirac. Dirac format aims to provide high-qualityDirac fermion (95 words) [view diff] no match in snippet view article find links to article

physics, a Dirac fermion is a fermion which is not its own antiparticle. It is named for Paul Dirac. They can be modelled with the Dirac equation. TheDirac equation (5,058 words) [view diff] no match in snippet view article find links to article

In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or includingDirac measure (550 words) [view diff] no match in snippet view article find links to article

Dirac measure assigns a size to a set based solely on whether it contains a fixed point x or not. It is one way of formalizing the idea of the Dirac deltaIncomplete Fermi–Dirac integral (32 words) [view diff] no match in snippet view article find links to article

incomplete Fermi–Dirac integral for an index j is given by This is an alternate definition of the incomplete polylogarithm. Complete Fermi–Dirac integralFeynman slash notation (191 words) [view diff] no match in snippet view article find links to article

study of Dirac fields in quantum field theory, Richard Feynman invented the convenient Feynman slash notation (less commonly known as the Dirac slash notation)Complete Fermi–Dirac integral (90 words) [view diff] no match in snippet view article find links to article

In mathematics, the complete Fermi–Dirac integral, named after Enrico Fermi and Paul Dirac, for an index j is given by This equals where is the polylogarithmDirac spinor (1,009 words) [view diff] no match in snippet view article find links to article

In quantum field theory, the Dirac spinor is the bispinor in the plane-wave solution of the free Dirac equation, where (in the units ) is a relativisticDirac delta function (8,126 words) [view diff] no match in snippet view article find links to article

uses, see Delta function (disambiguation). In mathematics, the Dirac delta function, or δ function, is a generalized function, or distributionGabriel Andrew Dirac (200 words) [view diff] no match in snippet view article find links to article

Gabriel Andrew Dirac (13 March 1925 – 20 July 1984) was a mathematician who mainly worked in graph theory. He stated a sufficient condition for a graphDirac operator (567 words) [view diff] no match in snippet view article find links to article

In mathematics and quantum mechanics, a Dirac operator is a differential operator that is a formal square root, or half-iterate, of a second-order operatorKapitsa–Dirac effect (770 words) [view diff] no match in snippet view article find links to article

The Kapitza–Dirac effect is a quantum mechanical effect consisting of the diffraction of matter by a standing wave of light. The effect was first predictedDirac equation in the algebra of physical space (540 words) [view diff] no match in snippet view article find links to article

The Dirac equation, as the relativistic equation that describes spin 1/2 particles in quantum mechanics can be written in terms of the Algebra of physicalDirac algebra (361 words) [view diff] no match in snippet view article find links to article

the Dirac algebra is the Clifford algebra Cℓ1,3(C). This was introduced by the mathematical physicist P. A. M. Dirac in 1928 in developing the Dirac equationDirac comb (877 words) [view diff] no match in snippet view article find links to article

In mathematics, a Dirac comb (also known as an impulse train and sampling function in electrical engineering) is a periodic tempered distribution constructedDirac sea (1,581 words) [view diff] no match in snippet view article find links to article

The Dirac sea is a theoretical model of the vacuum as an infinite sea of particles with negative energy. It was first postulated by the British physicistDirac, Charente (46 words) [view diff] no match in snippet view article find links to article

For other uses, see Dirac (disambiguation). Dirac is a commune in the Charente department in the Poitou-Charentes region in southwestern France. CommunesFermionic field (944 words) [view diff] no match in snippet view article find links to article

of a fermionic field is the Dirac field, which describes fermions with spin-1/2: electrons, protons, quarks, etc. The Dirac field can be described as eitherDirac string (341 words) [view diff] no match in snippet view article find links to article

physics, a Dirac string is a hypothetical one-dimensional curve in space, conceived of by the physicist Paul Dirac, stretching between two Dirac magneticDirac spectrum (97 words) [view diff] no match in snippet view article find links to article

In mathematics, a Dirac spectrum, named after Paul Dirac, is the spectrum of eigenvalues of a Dirac operator on a Riemannian manifold with a spin structureDirac adjoint (329 words) [view diff] no match in snippet view article find links to article

In quantum field theory, the Dirac adjoint defines the dual operation of a Dirac spinor. The Dirac adjoint is motivated by the need to form well-behavedDirac–von Neumann axioms (365 words) [view diff] no match in snippet view article find links to article

Dirac–von Neumann axioms give a mathematical formulation of quantum mechanics in terms of operators on a Hilbert space. They were introduced by Dirac (1930)Gamma matrices (2,910 words) [view diff] no match in snippet view article find links to article

In mathematical physics, the gamma matrices, , also known as the Dirac matrices, are a set of conventional matrices with specific anticommutation relationsDirac equation in curved spacetime (247 words) [view diff] no match in snippet view article find links to article

curved spacetime In mathematical physics, the Dirac equation in curved spacetime generalizes the original Dirac equation to curved space. It can be writtenList of things named after Paul Dirac (101 words) [view diff] no match in snippet view article find links to article

Paul Adrien Maurice Dirac. Dirac notation Dirac bracket Dirac adjoint Dirac field Dirac Lagrangian Dirac matrices Dirac sea Dirac constant, see reducedDirac large numbers hypothesis (2,063 words) [view diff] no match in snippet view article find links to article

The Dirac large numbers hypothesis (LNH) is an observation made by Paul Dirac in 1937 relating ratios of size scales in the Universe to that of forceAbraham–Lorentz force (1,744 words) [view diff] no match in snippet view article find links to article

of light. Its relativistic generalization is called the "Abraham–Lorentz–Dirac force". Both of these are in the domain of classical physics, not quantumThe Principles of Quantum Mechanics (350 words) [view diff] no match in snippet view article find links to article

monograph on quantum mechanics written by Paul Dirac and first published by Oxford University Press in 1930. Dirac gives an account of quantum mechanics byHelical Dirac fermion (59 words) [view diff] no match in snippet view article find links to article

A Helical Dirac fermion is a charge carrier that behaves as a massless relativistic particle with its intrinsic spin locked to its translational momentumDirac hole theory (175 words) [view diff] no match in snippet view article find links to article

Dirac hole theory is a theory in quantum mechanics, named after English theoretical physicist Paul Dirac. The theory poses that the continuum of negativePauli equation (567 words) [view diff] no match in snippet view article find links to article

external electromagnetic field. It is the non-relativistic limit of the Dirac equation and can be used where particles are moving at speeds much lessKronecker delta (1,271 words) [view diff] no match in snippet view article find links to article

Not to be confused with the Dirac delta function, nor with the Kronecker symbol. In mathematics, the Kronecker delta or Kronecker's delta, named afterClifford analysis (2,303 words) [view diff] no match in snippet view article find links to article

is the study of Dirac operators, and Dirac type operators in analysis and geometry, together with their applications. Examples of Dirac type operatorsFermion (1,002 words) [view diff] no match in snippet view article find links to article

a fermion (a name coined by Paul Dirac from the surname of Enrico Fermi) is any particle characterized by Fermi–Dirac statistics. These particles obeyThe Strangest Man (457 words) [view diff] no match in snippet view article find links to article

Strangest Man: The Hidden Life of Paul Dirac, Quantum Genius is a 2009 biography of quantum physicist Paul Dirac written by British physicist and authorNonlinear Dirac equation (712 words) [view diff] no match in snippet view article find links to article

notation. In quantum field theory, the nonlinear Dirac equation is a model of self-interacting Dirac fermions. This model is widely considered in quantumEinstein–Maxwell–Dirac equations (691 words) [view diff] no match in snippet view article find links to article

Einstein–Maxwell–Dirac equations (EMD) are related to quantum field theory. The current Big Bang Model is a quantum field theory in a curved spacetimeInteraction picture (897 words) [view diff] no match in snippet view article find links to article

In quantum mechanics, the interaction picture (also known as the Dirac picture) is an intermediate representation between the Schrödinger picture andBra–ket notation (3,837 words) [view diff] no match in snippet view article find links to article

the ket /kɛt/. The notation was introduced in 1939 by Paul Dirac and is also known as Dirac notation, though the notation has precursors in Grassmann'sTwo-body Dirac equations (3,898 words) [view diff] no match in snippet view article find links to article

subfields of quantum electrodynamics and quantum chromodynamics, the two-body Dirac equations (TBDE) of constraint dynamics provide a three-dimensional yetElectron magnetic moment (1,832 words) [view diff] no match in snippet view article find links to article

from the Dirac equation, a fundamental equation connecting the electron's spin with its electromagnetic properties. Reduction of the Dirac equation forMagnetic monopole (8,963 words) [view diff] no match in snippet view article find links to article

magnetic charge started with a paper by the physicist Paul A.M. Dirac in 1931. In this paper, Dirac showed that if any magnetic monopoles exist in the universePeriodic summation (203 words) [view diff] no match in snippet view article find links to article

summation of a Dirac delta function is the Dirac comb. Likewise, the periodic summation of an integrable function is its convolution with the Dirac comb. IfDirac bracket (3,147 words) [view diff] no match in snippet view article find links to article

The Dirac bracket is a generalization of the Poisson bracket developed by Paul Dirac to treat classical systems with second class constraints in HamiltonianParticle statistics (850 words) [view diff] no match in snippet view article find links to article

the assembly exist in the same state. Main article: Fermi–Dirac statistics In Fermi–Dirac statistics (F–D statistics) interchanging any two particlesAntiproton (1,159 words) [view diff] no match in snippet view article find links to article

predicted by Paul Dirac in his 1933 Nobel Prize lecture. Dirac received the Nobel Prize for his previous 1928 publication of his Dirac Equation that predictedZitterbewegung (590 words) [view diff] no match in snippet view article find links to article

motion of elementary particles, in particular electrons, that obey the Dirac equation. The existence of such motion was first proposed by Erwin SchrödingerBispinor (1,524 words) [view diff] no match in snippet view article find links to article

into each other. The Dirac bispinor is connected with the Weyl bispinor by a unitary transformation to the Dirac basis, The Dirac basis is the one mostKarnut (78 words) [view diff] no match in snippet view article find links to article

redirects here. For the village in Iran, see Dirak, Iran. For other uses, see Dirac (disambiguation). Coordinates: 40°47′01″N 43°57′15″E / 40.78361°N 43.95417°EBishop Road Primary School (83 words) [view diff] no match in snippet view article find links to article

primary school in Bristol, notable for having educated Cary Grant, Paul Dirac, John Polkinghorne and Ben J. Green. "Bishop Road Primary School InspectionWasp (novel) (1,233 words) [view diff] no match in snippet view article

registers the rebel organisation Dirac Angestun Gesept as a legitimate organisation: Title of organization: Dirac Angestun Gesept. Purpose of organization:Rarita–Schwinger equation (591 words) [view diff] no match in snippet view article find links to article

relativistic field equation of spin-3/2 fermions. It is similar to the Dirac equation for spin-1/2 fermions. This equation was first introduced by WilliamPositron (2,751 words) [view diff] no match in snippet view article find links to article

1928, Paul Dirac published a paper proposing that electrons can have both a positive charge and negative energy. This paper introduced the Dirac equationSpin geometry (107 words) [view diff] no match in snippet view article find links to article

differential geometry and topology where objects like spin manifolds and Dirac operators, and the various associated index theorems have come to play aPhoton (10,845 words) [view diff] no match in snippet view article find links to article

quantum theory. Dirac's work was the foundation of quantum electrodynamics, i.e., the quantization of the electromagnetic field itself. Dirac's approach isElectron (13,220 words) [view diff] no match in snippet view article find links to article

In 1928, building on Wolfgang Pauli's work, Paul Dirac produced a model of the electron – the Dirac equation, consistent with relativity theory, by applyingHiggsino (333 words) [view diff] no match in snippet view article find links to article

superpartner of the Higgs boson, as predicted by supersymmetry. The Higgsino is a Dirac fermion and that is a weak isodoublet with hypercharge half under the StandardPoint (geometry) (1,153 words) [view diff] no match in snippet view article

primitive together with the one of inclusion or connection. Main article: Dirac delta function Often in physics and mathematics, it is useful to think ofHydrogen-like atom (2,668 words) [view diff] no match in snippet view article find links to article

Schrödinger equation can be solved in analytic form, as can the (relativistic) Dirac equation. The solutions are one-electron functions and are referred to asBreit equation (711 words) [view diff] no match in snippet view article find links to article

relativistic wave equation derived by Gregory Breit in 1929 based on the Dirac equation, which formally describes two or more massive spin-1/2 particlesVan der Waerden notation (285 words) [view diff] no match in snippet view article find links to article

is represented as where In this notation the Dirac adjoint (also called the Dirac conjugate) is Dirac equation bra–ket notation Infeld–van der WaerdenMajorana fermion (2,495 words) [view diff] no match in snippet view article find links to article

Dirac fermion, which describes fermions that are not their own antiparticles. All of the Standard Model fermions except the neutrino behave as Dirac fermionsEnrico Fermi (9,686 words) [view diff] no match in snippet view article find links to article

to an ideal gas, employing a statistical formulation now known as Fermi–Dirac statistics. Today, particles that obey the exclusion principle are calledSterile neutrino (2,278 words) [view diff] no match in snippet view article find links to article

particles are initially massless under the Standard Model, since there are no Dirac mass terms in the Standard Model's Lagrangian. The only mass terms are generatedAnomalous magnetic dipole moment (939 words) [view diff] no match in snippet view article find links to article

result), can be calculated from the Dirac equation. It is usually expressed in terms of the g-factor; the Dirac equation predicts g = 2. For particlesFoldy–Wouthuysen transformation (2,845 words) [view diff] no match in snippet view article find links to article

Adolf Wouthuysen in 1949 to understand the nonrelativistic limit of the Dirac equation, the equation for the spin-1/2 particles. A detailed general discussionQuantum topology (129 words) [view diff] no match in snippet view article find links to article

mathematics that connects quantum mechanics with low-dimensional topology. Dirac notation provides a viewpoint of quantum mechanics which becomes amplifiedBargmann–Wigner equations (3,625 words) [view diff] no match in snippet view article find links to article

the first half of the twentieth century. Main article: Dirac equation For reference, the Dirac equation is summarized below. It is the basis for buildingDurrës (4,072 words) [view diff] no match in snippet view article find links to article

and Serbian empires. This is also the root of the Ottoman Turkish name Dıraç. In English usage, the Italian form Durazzo used to be widespread, but theThirring model (667 words) [view diff] no match in snippet view article find links to article

solvable quantum field theory which describes the self-interactions of a Dirac field in (1+1) dimensions. The Thirring model is given by the LagrangianRelativistic quantum mechanics (7,692 words) [view diff] no match in snippet view article find links to article

dynamics of charged particles in electromagnetic fields. The key result is the Dirac equation, from which these predictions emerge automatically. By contrastPrimary constraint (412 words) [view diff] no match in snippet view article find links to article

forget about the distinction between primary and secondary constraints. Dirac (1964, p.43) In Hamiltonian mechanics, a primary constraint is a relationProbability of occupation (51 words) [view diff] no match in snippet view article find links to article

energy level to be occupied. Fermions such as electrons follow a Fermi–Dirac distribution and bosons such as phonons and photons follow a Bose–EinsteinLamb shift (963 words) [view diff] no match in snippet view article find links to article

of the hydrogen atom in quantum electrodynamics (QED). According to the Dirac equation, the 2S1/2 and 2P1/2 orbitals should have the same energy. However't Hooft–Polyakov monopole (463 words) [view diff] no match in snippet view article find links to article

the 't Hooft–Polyakov monopole is a topological soliton similar to the Dirac monopole but without any singularities. It arises in the case of a Yang–MillsYukawa interaction (643 words) [view diff] no match in snippet view article find links to article

named after Hideki Yukawa, is an interaction between a scalar field ϕ and a Dirac field ψ of the type (scalar) or (pseudoscalar). The Yukawa interactionList of mathematical topics in quantum theory (351 words) [view diff] no match in snippet view article find links to article

entanglement spinor, spinor group, spinor bundle Dirac sea Spin foam Poincaré group gamma matrices Dirac adjoint Wigner's classification anyon CopenhagenCanonical quantum gravity (2,715 words) [view diff] no match in snippet view article find links to article

quantization techniques for constrained Hamiltonian systems invented by Paul Dirac.[3] Dirac's approach allows the quantization of systems that include gauge symmetriesRelativistic wave equations (2,068 words) [view diff] no match in snippet view article find links to article

were comfortable with the "Dirac sea" of negative energy states). The natural problem became clear: to generalize the Dirac equation to particles withFermi surface (1,073 words) [view diff] no match in snippet view article find links to article

Consider a spinless ideal Fermi gas of particles. According to Fermi–Dirac statistics, the mean occupation number of a state with energy is givenKogut–Susskind fermion (89 words) [view diff] no match in snippet view article find links to article

Kogut–Susskind fermions are a lattice version of Kähler–Dirac fermions, which obey a first-order differential equation by taking an alternative[clarificationGlobal symmetry (82 words) [view diff] no match in snippet view article find links to article

the (for a constant - making it a global transformation) group on the Dirac Lagrangian: Under this transformation the wavefunction changes as andYCgCo (463 words) [view diff] no match in snippet view article find links to article

This is supported by video compression codecs such as H.264/MPEG-4 AVC and Dirac since it can losslessly be converted to and from RGB with fewer bits requiredAntiparticle (1,974 words) [view diff] no match in snippet view article find links to article

an infinite negative charge for the universe--a problem of which Dirac was aware. Dirac tried[clarification needed] to argue that we would perceive thisFeynman parametrization (254 words) [view diff] no match in snippet view article find links to article

which simplifies evaluating integrals like: More generally, using the Dirac delta function: Even more generally, provided that for all : See alsoMajorana equation (300 words) [view diff] no match in snippet view article find links to article

The Majorana equation is a relativistic wave equation similar to the Dirac equation but includes the charge conjugate ψc of a spinor ψ. It is named afterKlein–Gordon equation (1,481 words) [view diff] no match in snippet view article find links to article

particle propagates both forwards and backwards in time. Any solution to the Dirac equation is automatically a solution to the Klein–Gordon equation, but theFermi gas (624 words) [view diff] no match in snippet view article find links to article

fermions. Fermions, named after Enrico Fermi, are particles that obey Fermi–Dirac statistics. These statistics determine the energy distribution of fermionsSupport (measure theory) (1,234 words) [view diff] no match in snippet view article

line R. It seems clear that λ "lives on" the whole of the real line. A Dirac measure δp at some point p ∈ R. Again, intuition suggests that the measureJoseph Polchinski (500 words) [view diff] no match in snippet view article find links to article

to theoretical physics, D-branes are the best known. In 2008 he won the Dirac Medal for his work in superstring theory. In 1990, commenting on the NovikovCumrun Vafa (327 words) [view diff] no match in snippet view article find links to article

first joined as a Harvard Junior Fellow. He is the recipient of the 2008 Dirac Medal. Cumrun Vafa was born in Tehran, Iran in 1960. He graduated fromLaplacian of the indicator (3,064 words) [view diff] no match in snippet view article find links to article

indicator of the domain D is a generalisation of the derivative of the Dirac delta function to higher dimensions, and is non-zero only on the surfaceGross–Neveu model (699 words) [view diff] no match in snippet view article find links to article

The Gross-Neveu model is a quantum field theory model of Dirac fermions interacting via four fermion interactions in 1 spatial and 1 time dimension. ItWolfgang Pauli (3,049 words) [view diff] no match in snippet view article find links to article

sometimes said to have influenced Paul Dirac in his creation of the Dirac equation for the relativistic electron, though Dirac stated that he invented these sameThirring–Wess model (273 words) [view diff] no match in snippet view article find links to article

an exactly solvable quantum field theory describing the interaction of a Dirac field with a vector field in dimension two. The Lagrangian density isSoler model (290 words) [view diff] no match in snippet view article find links to article

The Soler model is a quantum field theory model of Dirac fermions interacting via four fermion interactions in 3 spatial and 1 time dimension. It wasRalph H. Fowler (653 words) [view diff] no match in snippet view article find links to article

made a Fellow of the Royal Society. He became research supervisor to Paul Dirac and, in 1926, worked with him on the statistical mechanics of white dwarfJohn Cardy (392 words) [view diff] no match in snippet view article find links to article

received the Dirac Medal of the IoP in 2000, was awarded the Lars Onsager Prize by the APS in 2004, the Boltzmann Medal by IUPAP in 2010, and the Dirac MedalBoson (1,592 words) [view diff] no match in snippet view article find links to article

particles, the other being fermions. The name boson was coined by Paul Dirac to commemorate the contribution of the Indian physicist Satyendra Nath BoseParastatistics (779 words) [view diff] no match in snippet view article find links to article

better known particle statistics models (Bose–Einstein statistics, Fermi–Dirac statistics and Maxwell–Boltzmann statistics). Other alternatives includeG-factor (physics) (1,029 words) [view diff] no match in snippet view article

charged, spin-1/2 particle that does not possess any internal structure (a Dirac particle) is given by where μ is the spin magnetic moment of the particleChiral anomaly (959 words) [view diff] no match in snippet view article find links to article

state with some particles in the other vacuum. In particular, there is a Dirac sea of fermions and, when such a tunneling happens, it causes the energyFirst-order hold (715 words) [view diff] no match in snippet view article find links to article

necessary because, in the sampling and reconstruction theorem, a sequence of dirac impulses, xs(t), representing the discrete samples, x(nT), is low-pass filteredDavid Olive (159 words) [view diff] no match in snippet view article find links to article

University to help set up the new theoretical physics group. He was awarded the Dirac Prize and Medal of the International Centre for Theoretical Physics in 1997Theodore James Courant (195 words) [view diff] no match in snippet view article find links to article

contributions to the study of Dirac manifolds, which generalize both symplectic manifolds and Poisson manifolds, and are related to the Dirac theory of constraintsValuation (measure theory) (656 words) [view diff] no match in snippet view article

called Dirac valuation. This concept bears its origin from distribution theory as it is an obvious transposition to valuation theory of Dirac distribution:Incomplete polylogarithm (76 words) [view diff] no match in snippet view article find links to article

the polylogarithm function. It is sometimes known as the incomplete Fermi–Dirac integral or the incomplete Bose–Einstein integral. It may be defined by:Lucasian Professor of Mathematics (308 words) [view diff] no match in snippet view article find links to article

include Isaac Newton, Joseph Larmor, Charles Babbage, George Stokes, Paul Dirac and Stephen Hawking. Lucas, in his will, bequeathed his library of 4,000Zero-order hold (623 words) [view diff] no match in snippet view article find links to article

impulse response equal to a rect function, and with input being a sequence of dirac impulses scaled to the sample values. The filter can then be analyzed inELKO field (231 words) [view diff] no match in snippet view article find links to article

scalar-like mass dimension they differ significantly from the mass dimension 3/2 Dirac fermions. An up-to-date reference is a 2013 preprint. D.V. AhluwaliaJ. Robert Oppenheimer Memorial Prize (575 words) [view diff] no match in snippet view article find links to article

speech for the inaugural award to Dirac was published as The Development of Quantum Theory (1971). 1969 – Paul Dirac 1970 – Freeman Dyson 1971 – AbdusSpacetime algebra (1,427 words) [view diff] no match in snippet view article find links to article

Thus , , otherwise . The basis vectors share these properties with the Dirac matrices, but no explicit matrix representation is utilized in STA. ThisHelicity basis (257 words) [view diff] no match in snippet view article find links to article

and are the momentum-space Dirac spinors for a fermion and anti-fermion respectively. Put it more explicitly, the Dirac spinors in the helicity basisRajiah Simon (99 words) [view diff] no match in snippet view article find links to article

by working out the focusing action of a magnetic quadrupole using the Dirac Equation. HANDBOOK OF SHANTI SWARUP BHATNAGAR PRIZE WINNERS ( 1958 -Dyon (257 words) [view diff] no match in snippet view article find links to article

Schwinger in 1969 as a phenomenological alternative to quarks. He extended the Dirac quantization condition to the dyon and used the model to predict the existenceFierz identity (213 words) [view diff] no match in snippet view article find links to article

physicist Markus Fierz. There is a version of the Fierz identities for Dirac spinors and there is another version for Weyl spinors. And there are versionsSilicene (2,512 words) [view diff] no match in snippet view article find links to article

Silicene and graphene have similar electronic structures. Both have a Dirac cone and linear electronic dispersion around the k point. Both also haveCanonical quantization (2,939 words) [view diff] no match in snippet view article find links to article

quite Werner Heisenberg's route to obtaining quantum mechanics, but Paul Dirac introduced it in his 1926 doctoral thesis, the "method of classical analogy"Chirality (physics) (2,267 words) [view diff] no match in snippet view article

transformation between the two is called parity. Invariance under parity by a Dirac fermion is called chiral symmetry. An experiment on the weak decay of cobalt-60C-number (131 words) [view diff] no match in snippet view article find links to article

term c-number (or classical number) is an old nomenclature used by Paul Dirac which refers to real and complex numbers. It is used to distinguish fromQuantum electrodynamics (5,073 words) [view diff] no match in snippet view article find links to article

British scientist Paul Dirac, who (during the 1920s) was able to compute the coefficient of spontaneous emission of an atom. Dirac described the quantizationSpinor bundle (222 words) [view diff] no match in snippet view article find links to article

(2000), Dirac Operators in Riemannian Geometry, American Mathematical Society, ISBN 978-0-8218-2055-1 page 53 Friedrich, Thomas (2000), Dirac OperatorsQuantum mechanics (10,532 words) [view diff] no match in snippet view article find links to article

Compton, Albert Einstein, Erwin Schrödinger, Max Born, John von Neumann, Paul Dirac, Enrico Fermi, Wolfgang Pauli, Max von Laue, Freeman Dyson, David HilbertKilling spinor (312 words) [view diff] no match in snippet view article find links to article

spinor indicates those twistor spinors which are also eigenspinors of the Dirac operator. The term is named after Wilhelm Killing. Another equivalent definitionMildred Dresselhaus (2,027 words) [view diff] no match in snippet view article find links to article

construct various Dirac-cone materials, including single-Dirac-cone materials, bi-Dirac-cone materials, tri-Dirac-cone materials, quasi-Dirac-cone materialsBargmann's limit (53 words) [view diff] no match in snippet view article find links to article

number Nl of bound states in a system. It takes the form Note that the Dirac delta function potential attains this limit. Bargmann, Proc. Nat. AcadHistory of quantum field theory (3,645 words) [view diff] no match in snippet view article find links to article

physics, the history of quantum field theory starts with its creation by Paul Dirac, when he attempted to quantize the electromagnetic field in the late 1920sBlack star (semiclassical gravity) (447 words) [view diff] no match in snippet view article

Einstein-Maxwell-Dirac equations system, which is the (super)classical limit of quantum electrodynamics, and for the Einstein-Yang-Mills-Dirac system, whichA System of Logic (228 words) [view diff] no match in snippet view article find links to article

the history of science, being a strong influence on scientists such as Dirac. Mill, John Stuart, A System of Logic, University Press of the PacificAdric (1,286 words) [view diff] no match in snippet view article find links to article

name Adric is an anagram derived from Nobel Prize-winning physicist Paul Dirac. Waterhouse is the youngest male actor to play a companion so far in theHeaviside step function (974 words) [view diff] no match in snippet view article find links to article

function: The Heaviside function can also be defined as the integral of the Dirac delta function: H′ = δ. This is sometimes written as although this expansionList of scientific constants named after people (431 words) [view diff] no match in snippet view article find links to article

constant () – Max Planck Reduced Planck constant or Dirac constant (-bar, ħ) – Max Planck, Paul Dirac Ramanujan–Soldner constant – Srinivasa RamanujanMonopole (173 words) [view diff] no match in snippet view article find links to article

Monopole may refer to: Magnetic monopole, or Dirac monopole, a hypothetical particle that may be loosely described as a magnet with only one pole, orFirst class constraint (2,994 words) [view diff] no match in snippet view article find links to article

calculated previously, and their Dirac brackets generated. First and second class constraints were introduced by Dirac (1950, p.136, 1964, p.17) as a waySatyendra Nath Bose (2,606 words) [view diff] no match in snippet view article find links to article

that obey Bose–Einstein statistics, bosons, was named after Bose by Paul Dirac. A self-taught scholar and a polyglot, he had a wide range of interestsTransformation theory (quantum mechanics) (250 words) [view diff] no match in snippet view article

transformation theory refers to a procedure and a "picture" used by P. A. M. Dirac in his early formulation of quantum theory, from around 1927. This "transformation"Feynman checkerboard (1,166 words) [view diff] no match in snippet view article find links to article

one spatial dimension. It provides a representation of solutions of the Dirac equation in (1+1)-dimensional spacetime as discrete sums. The model canNarasimhaiengar Mukunda (182 words) [view diff] no match in snippet view article find links to article

by working out the focusing action of a magnetic quadrupole using the Dirac Equation. "Twisted Gaussian Schell-model beams. I & II. Symmetry structureSpin quantum number (1,520 words) [view diff] no match in snippet view article find links to article

light for the magnetic moment to be of the observed strength. In 1930, Paul Dirac developed a new version of the Wave Equation which was relativisticallyLagrangian (field theory) (1,976 words) [view diff] no match in snippet view article

form. The Lagrangian density for a Dirac field is: where ψ is a Dirac spinor (annihilation operator), is its Dirac adjoint (creation operator), andSpin (physics) (5,803 words) [view diff] no match in snippet view article

Paul Dirac published the Dirac equation, which described the relativistic electron. In the Dirac equation, a four-component spinor (known as a "Dirac spinor")Léon Rosenfeld (114 words) [view diff] no match in snippet view article find links to article

work in quantum electrodynamics that predates by two decades the work by Dirac and Bergmann. He coined the name lepton. In 1949 Léon Rosenfeld was awardedPositronium (1,625 words) [view diff] no match in snippet view article find links to article

using finite element methods of J. Shertzer. The Dirac equation whose Hamiltonian comprises two Dirac particles and a static Coulomb potential is not relativisticallyGiorgio Parisi (967 words) [view diff] no match in snippet view article find links to article

Giorgio Parisi has been awarded several honors; the Boltzmann Medal and the Dirac Medal. He is one of the two Italian physicists to be member of the AmericanMoyal bracket (964 words) [view diff] no match in snippet view article find links to article

succeeded in publishing his work in 1949 after a lengthy dispute with Paul Dirac. In the meantime this idea was independently introduced in 1946 by Hip GroenewoldSchwinger model (187 words) [view diff] no match in snippet view article find links to article

2D (1 spatial dimension + time) Euclidean quantum electrodynamics with a Dirac fermion. This model exhibits a spontaneous symmetry breaking of the U(1)Hamiltonian (quantum mechanics) (2,366 words) [view diff] no match in snippet view article

principle of detailed balance. However, in the more general formalism of Dirac, the Hamiltonian is typically implemented as an operator on a Hilbert spaceCurtis Callan (240 words) [view diff] no match in snippet view article find links to article

instanton physics and to the theory of monopoles and strings") and the Dirac Medal in 2004. Callan received his B.Sc. in physics from Haverford CollegeMichele Parrinello (301 words) [view diff] no match in snippet view article find links to article

movements of atoms and molecules). Parrinello and Roberto Car were awarded the Dirac Medal and the Sidney Fernbach Award in 2009 for their continuing developmentParticle physics (2,518 words) [view diff] no match in snippet view article find links to article

Chadwick · Bose · Sudarshan · Koshiba · Davis, Jr. · Anderson · Fermi · Dirac · Feynman · Rubbia · Gell-Mann · Kendall · Taylor · Friedman · Powell ·Greg Moore (physicist) (323 words) [view diff] no match in snippet view article

physics and four-manifold theory." In 2015, he was jointly awarded the 2015 Dirac Medal by ICTP. Moore was a member of the Advisory Board for Springer'sMathematical formulation of quantum mechanics (4,667 words) [view diff] no match in snippet view article find links to article

Jordan, and the foundational work of John von Neumann, Hermann Weyl and Paul Dirac, and it became possible to unify several different approaches in terms ofThermal de Broglie wavelength (666 words) [view diff] no match in snippet view article find links to article

wavelength; in this case the gas will obey Bose–Einstein statistics or Fermi–Dirac statistics, whichever is appropriate. This is for example the case for electronsQuasi Fermi level (698 words) [view diff] no match in snippet view article find links to article

function of the electrons at the energy level of E is presented by Fermi–Dirac distribution function. In this case the Fermi level is defined as the levelZirconium(II) hydride (161 words) [view diff] no match in snippet view article

low temperature. Zirconium(II) hydride has repeatedly been the subject of Dirac–Hartree–Fock relativistic calculation studies, which investigate the stabilitiesOggConvert (246 words) [view diff] no match in snippet view article find links to article

various types into the free Ogg Vorbis audio format, and the Theora, VP8 and Dirac video formats. It supports Ogg, Matroska and WebM containers for outputLothar Wolfgang Nordheim (244 words) [view diff] no match in snippet view article find links to article

with the help of the assumption that electrons in metals obeyed Fermi-Dirac statistics, derived an (approximate) emission equation. Over time, thisPlanck constant (6,519 words) [view diff] no match in snippet view article find links to article

constant. The resulting constant is called the reduced Planck constant or Dirac constant. It is equal to the Planck constant divided by 2π, and is denotedRelativistic particle (191 words) [view diff] no match in snippet view article find links to article

relativistic particles, with a prominent example being postulations through Dirac equations of single particle motion. Massive particles are relativisticRajagopalan Parthasarathy (153 words) [view diff] no match in snippet view article find links to article

discrete series of representations of a semisimple Lie group in the space of Dirac Spinors. He made considerable progress in many central problems in representationExotic probability (170 words) [view diff] no match in snippet view article find links to article

the quaternions. Youssef also cites the work of Richard Feynman, P. A. M. Dirac, Stanley Gudder and S. K. Srinivasan as relevant to exotic probability theoriesHydrogen atom (2,994 words) [view diff] no match in snippet view article find links to article

solutions it yields for the hydrogen atom are not entirely correct. The Dirac equation of relativistic quantum theory improves these solutions (see below)Index of physics articles (D) (1,782 words) [view diff] no match in snippet view article

Diproton Diquark Dirac Prize Dirac adjoint Dirac delta function Dirac equation Dirac equation in the algebra of physical space Dirac fermion Dirac large numbersJogesh Pati (372 words) [view diff] no match in snippet view article find links to article

Retrieved 24 April 2012. received the Dirac Medal for the year 2000 (with Howard Georgi and Helen Quinn). "Dirac medal goes to particle theorists - physicsworldGraphene (19,200 words) [view diff] no match in snippet view article find links to article

understanding the electronic properties of 3D graphite. The emergent massless Dirac equation was first pointed out by Gordon Walter Semenoff and David P. DeVincenzoTheora (2,832 words) [view diff] no match in snippet view article find links to article

other codecs. It is comparable in open standards philosophy to the BBC's Dirac codec. Theora is named after Theora Jones, Edison Carter's Controller onJames Bjorken (388 words) [view diff] no match in snippet view article find links to article

the Fermi National Accelerator Laboratory (1979–1989). He was awarded the Dirac Medal of the ICTP in 2004 and in 2015 the Wolf Prize in Physics. BjorkenFundamental solution (603 words) [view diff] no match in snippet view article find links to article

distribution theory of the older idea of a Green's function. In terms of the Dirac delta "function" δ(x), a fundamental solution F is the solution of the inhomogeneousHigher-dimensional gamma matrices (834 words) [view diff] no match in snippet view article find links to article

generalize to arbitrary dimension the four-dimensional Gamma matrices of Dirac, which are a mainstay of relativistic quantum mechanics. They are utilizedKlein transformation (327 words) [view diff] no match in snippet view article find links to article

commutation/anticommutation relations until we're done. This explains the equivalence between parastatistics and the more familiar Bose–Einstein/Fermi–Dirac statistics.Laurent Schwartz (1,211 words) [view diff] no match in snippet view article find links to article

distributions, which gives a well-defined meaning to objects such as the Dirac delta function. He was awarded the Fields Medal in 1950 for his work onState space (physics) (166 words) [view diff] no match in snippet view article

vectors, using Dirac's bra–ket notation, can often be treated like coordinate vectors and operated on using the rules of linear algebra. This Dirac formalismCausal fermion system (2,771 words) [view diff] no match in snippet view article find links to article

is the fact that the Dirac equation in Minkowski space has solutions of negative energy which are usually associated to the Dirac sea. Taking the conceptKlein paradox (729 words) [view diff] no match in snippet view article find links to article

1929, physicist Oskar Klein obtained a surprising result by applying the Dirac equation to the familiar problem of electron scattering from a potentialStochastic interpretation (201 words) [view diff] no match in snippet view article find links to article

Phase-space Schrödinger Sum-over-histories (path integral) Equations Dirac Klein–Gordon Pauli Rydberg Schrödinger Interpretations OverviewComparison of video codecs (2,688 words) [view diff] no match in snippet view article find links to article

Retrieved 2009-10-06 Theora.org FAQ: what is the license for Theora? Dirac Video Compression, Retrieved on 2009-08-08 x264 - a free h264/avc encoderDelta potential (1,676 words) [view diff] no match in snippet view article find links to article

the delta potential is a potential well mathematically described by the Dirac delta function - a generalized function. Qualitatively, it corresponds toAnyon (1,867 words) [view diff] no match in snippet view article find links to article

bosons, according to their statistical behaviour. Fermions obey the Fermi–Dirac statistics while bosons obey the Bose–Einstein statistics. In the languageFermi energy (1,601 words) [view diff] no match in snippet view article find links to article

a typical value for the Fermi energy is usually given as 38 MeV. Fermi–Dirac statistics: the distribution of electrons over stationary states for a non-interactingModern physics (534 words) [view diff] no match in snippet view article find links to article

to account for the observed behaviour of the gas, and the (modern) Fermi–Dirac or Bose–Einstein distributions have to be used instead. German physicistLichnerowicz formula (280 words) [view diff] no match in snippet view article find links to article

1963, and Roland Weitzenböck. The formula gives a relationship between the Dirac operator and the Laplace–Beltrami operator acting on spinors, in which theWomen in Somalia (1,108 words) [view diff] no match in snippet view article find links to article

like Eid, women wear the dirac, a long, light, diaphanous voile dress made of cotton, polyester or saree fabric. The dirac is related to the short-sleevedSign function (582 words) [view diff] no match in snippet view article find links to article

distribution theory, the derivative of the signum function is two times the Dirac delta function, which can be demonstrated using the identity (where H(x)Center for Theoretical Studies, University of Miami (288 words) [view diff] no match in snippet view article find links to article

Among others, the long term resident members of the Center included Paul Dirac (1969–1972) and Lars Onsager (1972–1976), while the affiliated faculty includedNambu–Jona-Lasinio model (680 words) [view diff] no match in snippet view article find links to article

complicated effective theory of nucleons and mesons constructed from interacting Dirac fermions with chiral symmetry, paralleling the construction of Cooper pairsFermi level (2,975 words) [view diff] no match in snippet view article find links to article

it generally provides correct results when applied correctly. The Fermi–Dirac distribution gives the probability that (at thermodynamic equilibrium)M-theory (7,549 words) [view diff] no match in snippet view article find links to article

called branes. Such objects had been considered as early as 1962 by Paul Dirac, and they were reconsidered by a small but enthusiastic group of physicistsPeriodic table (10,382 words) [view diff] no match in snippet view article find links to article

inaccurate when applied to such an element. Relativistic Dirac equation The relativistic Dirac equation has problems for elements with more than 137 protonsWrapped distribution (881 words) [view diff] no match in snippet view article find links to article

written as the convolution of the "unwrapped" distribution and a Dirac comb: The Dirac comb may also be expressed as a sum of exponentials, so we may write:N-slit interferometric equation (1,226 words) [view diff] no match in snippet view article find links to article

applied to optics, and interference in particular, by Paul Dirac. Feynman, in his lectures, uses Dirac's notation to describe thought experiments on double-slit