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Longer titles found: Exterior covariant derivative (view), Gauge covariant derivative (view), Second covariant derivative (view)

searching for Covariant derivative 42 found (278 total)

alternate case: covariant derivative

Yang–Mills–Higgs equations (449 words) [view diff] exact match in snippet view article find links to article

|(x)=1} where A is a connection on a vector bundle, DA is the exterior covariant derivative, FA is the curvature of that connection, Φ is a section of that vector

Geometric calculus (3,026 words) [view diff] exact match in snippet view article find links to article

itself is not necessarily on the manifold. Therefore, we define the covariant derivative to be the forced projection of the intrinsic derivative back onto

Schwinger model (346 words) [view diff] exact match in snippet view article find links to article

Dμ=∂μ−iAμ{\displaystyle D_{\mu }=\partial _{\mu }-iA_{\mu }} is the gauge covariant derivative, ψ{\displaystyle \psi } is the fermion spinor, m{\displaystyle m}

Spin connection (2,445 words) [view diff] exact match in snippet view article find links to article

b}+\Gamma _{\ \sigma \mu }^{\nu }e^{\sigma b})} using the gravitational covariant derivative ∂;μeνb{\displaystyle \partial _{;\mu }e^{\nu b}} of the contravariant

Komar superpotential (342 words) [view diff] exact match in snippet view article find links to article

_{\rho }}, and where ∇σ{\displaystyle \nabla _{\sigma }} denotes covariant derivative with respect to the Levi-Civita connection. The Komar two-form: U(LG

Normal coordinates (1,200 words) [view diff] exact match in snippet view article find links to article

manifold with a symmetric affine connection. In such coordinates the covariant derivative reduces to a partial derivative (at p only), and the geodesics through

Coleman–Weinberg potential (752 words) [view diff] exact match in snippet view article find links to article

{\displaystyle D_{\mu }=\partial _{\mu }-\mathrm {i} (e/\hbar c)A_{\mu }} the covariant derivative containing the electric charge e {\displaystyle e} of the electromagnetic

Double tangent bundle (1,572 words) [view diff] exact match in snippet view article find links to article

is called a (nonlinear) covariant derivative on M. The term nonlinear refers to the fact that this kind of covariant derivative DX on is not necessarily

Tetradic Palatini action (3,523 words) [view diff] exact match in snippet view article find links to article

to introduce an appropriate derivative (covariant derivative). We introduce an arbitrary covariant derivative via DαVI=∂αVI+ωαIJVJ.{\displaystyle {\mathcal

Metric-affine gravitation theory (1,122 words) [view diff] exact match in snippet view article find links to article

with torsion where a linear connection obeys the condition that a covariant derivative of a metric equals zero. Metric-affine gravitation theory straightforwardly

Higgs mechanism (6,713 words) [view diff] exact match in snippet view article find links to article

\psi \ ,} where again the gauge field A only enters via the gauge covariant derivative operator Dμ (i.e., it is only indirectly visible). The quantities

Conformal Killing vector field (1,177 words) [view diff] exact match in snippet view article find links to article

\nabla } is the Levi Civita derivative of g{\displaystyle g} (aka covariant derivative), and X♭=g(X,⋅){\displaystyle X^{\flat }=g(X,\cdot )} is the dual

Scalar electrodynamics (879 words) [view diff] exact match in snippet view article find links to article

D_{\mu }\phi =(\partial _{\mu }\phi -ieA_{\mu }\phi )} is the covariant derivative of the field ϕ{\displaystyle \phi } e=−|e|<0{\displaystyle e=-|e|<0}

Newton–Cartan theory (1,255 words) [view diff] exact match in snippet view article find links to article

are as described, ∇{\displaystyle \nabla } is a metrics-compatible covariant derivative operator; and the metrics satisfy the orthogonality condition. One

Vanishing scalar invariant spacetime (357 words) [view diff] exact match in snippet view article find links to article

which the Karlhede invariant classification requires the fourth covariant derivative of the Riemann tensor", Classical and Quantum Gravity, 9 (10): L143

Optical scalars (2,375 words) [view diff] exact match in snippet view article find links to article

Use hba{\displaystyle h_{\;\;b}^{a}} to project the coordinate covariant derivative ∇bZa{\displaystyle \nabla _{b}Z_{a}} and one obtains the "spatial"

Dirac equation (11,971 words) [view diff] exact match in snippet view article find links to article

scalar electrodynamics: the partial derivative is promoted to a covariant derivative Dμ{\displaystyle D_{\mu }} Dμψ=∂μψ+ieAμψ,{\displaystyle D_{\mu }\psi

Fermi–Walker transport (804 words) [view diff] exact match in snippet view article find links to article

{DV}{ds}}\right)V+(X,V){\frac {DV}{ds}},} where V is four-velocity, D is the covariant derivative, and (⋅,⋅){\displaystyle (\cdot ,\cdot )} is the scalar product.

Scalar chromodynamics (1,095 words) [view diff] exact match in snippet view article find links to article

is the curvature form. D μ ϕ {\displaystyle D_{\mu }\phi } is the covariant derivative of ϕ {\displaystyle \phi } , defined as D μ ϕ = ∂ μ ϕ − i g ρ ( A

Michio Jimbo (294 words) [view diff] exact match in snippet view article find links to article

of the theory of isomonodromic deformation systems for rational covariant derivative operators. In 1993 he won the Japan Academy Prize for this work.

Spacetime symmetries (1,455 words) [view diff] exact match in snippet view article find links to article

symmetric (0,2)-tensor field T such that the total symmetrization of its covariant derivative vanishesPages displaying wikidata descriptions as a fallback Lie

Supersymmetric gauge theory (1,554 words) [view diff] exact match in snippet view article find links to article

gauge connection A. In the analytic basis for the tangent space, the covariant derivative is given by DM=dM+iqAM{\displaystyle D_{M}=d_{M}+iqA_{M}}. Integrability

Diamagnetism (2,261 words) [view diff] exact match in snippet view article find links to article

Mathematical inequality relating the derivative of a function to its covariant derivative Gerald Küstler (2007). "Diamagnetic Levitation – Historical Milestones"

Supermultiplet (1,958 words) [view diff] exact match in snippet view article find links to article

{\overline {D}}\Phi =0}, where D¯{\displaystyle {\bar {D}}} is the covariant derivative, given in index notation as D¯α˙=−∂¯α˙−iθασαα˙μ∂μ.{\displaystyle

Hessian matrix (3,251 words) [view diff] exact match in snippet view article find links to article

f=\nabla df,} where this takes advantage of the fact that the first covariant derivative of a function is the same as its ordinary differential. Choosing

Lie algebra cohomology (2,162 words) [view diff] exact match in snippet view article find links to article

Chevalley–Eilenberg differential may then be thought of as a restriction of the covariant derivative on the trivial fiber bundle G×M→G{\displaystyle G\times M\rightarrow

Komar mass (1,947 words) [view diff] exact match in snippet view article find links to article

\tau } is the proper time. In curved space-time, we must take the covariant derivative. Thus we compute the acceleration vector as: ab=∇uub=uc∇cub{\displaystyle

Spray (mathematics) (2,169 words) [view diff] exact match in snippet view article

Bucătaru and Miron. Of particular note is their concept of a dynamic covariant derivative. In another paper Bucătaru, Constantinescu and Dahl relate this concept

Fréchet space (4,947 words) [view diff] exact match in snippet view article find links to article

{\displaystyle V.} If s{\displaystyle s} is a section, denote its jth covariant derivative by Djs.{\displaystyle D^{j}s.} Then ‖s‖n=∑j=0nsupx∈M|Djs|{\displaystyle

Harmonic coordinates (2,547 words) [view diff] exact match in snippet view article find links to article

partitions of unity as well. For instance, to control the second covariant derivative of a function by a locally defined second partial derivative, it

Bumblebee models (3,093 words) [view diff] exact match in snippet view article find links to article

\end{aligned}}} In this expression, Dμ{\displaystyle D_{\mu }{\Big .}} is the covariant derivative, Bμν=DμBν−DνBμ{\displaystyle B_{\mu \nu }=D_{\mu }B_{\nu }-D_{\nu

Glossary of string theory (5,157 words) [view diff] exact match in snippet view article find links to article

' (prime) X′ means ∂X/∂σ. dot above letter Ẋ means ∂X/∂τ ∇ 1. A covariant derivative 2. The del operator. □ The D'Alembert operator, or non-Euclidean

Paneitz operator (2,261 words) [view diff] exact match in snippet view article find links to article

Webster-Tanaka Torsion tensor and ϕ1{\displaystyle \phi _{1}} the covariant derivative of the function ϕ{\displaystyle \phi } with respect to the Webster-Tanaka

Holonomy (5,657 words) [view diff] exact match in snippet view article find links to article

presence of parallel spinors, meaning spinor fields with vanishing covariant derivative. In particular, the following facts hold: Hol(ω) ⊂ U(n) if and only

Spacetime algebra (5,961 words) [view diff] exact match in snippet view article find links to article

{\frac {d}{d\tau }}R={\frac {1}{2}}(\Omega -\omega )R} and the covariant derivative Dτ=∂τ+12ω,{\displaystyle D_{\tau }=\partial _{\tau }+{\frac {1}{2}}\omega

Vasiliev equations (9,055 words) [view diff] exact match in snippet view article find links to article

}}}}\right)C=0\,,} where ∇{\displaystyle \nabla } is the Lorentz covariant derivative ∇=d−ϖαβ(yα∂∂yβ+yβ∂∂yα)−...{\displaystyle \nabla =d-\varpi ^{\alpha

Hamiltonian constraint of LQG (6,931 words) [view diff] exact match in snippet view article find links to article

\omega _{\mu }^{IJ}} that allows us to gauge the Lorentz group. The covariant derivative defined with the spin connection is, ∇aψ=(∂a−i4ωaIJσIJ)ψ{\displaystyle

Loop quantum gravity (15,817 words) [view diff] exact match in snippet view article find links to article

Aai{\displaystyle A_{a}^{i}} is called the chiral spin connection. It defines a covariant derivative Da{\displaystyle {\mathcal {D}}_{a}}. It turns out that E~ia{\displaystyle

De Broglie–Bohm theory (16,410 words) [view diff] exact match in snippet view article find links to article

_{k}-{\frac {ie_{k}}{\hbar }}\mathbf {A} (\mathbf {q} _{k})} is the covariant derivative, involving the vector potential, ascribed to the coordinates of k{\displaystyle

Majorana equation (8,038 words) [view diff] exact match in snippet view article find links to article

spinor bundle. Decomposed into distinct terms, it includes the usual covariant derivative d+A.{\displaystyle d+A.} The A{\displaystyle A} field can be seen

Loop representation in gauge theories and quantum gravity (5,111 words) [view diff] exact match in snippet view article find links to article

(x)} are not covariant under this transformation. We introduce a covariant derivative Dμ=I∂μ+igAμ(x){\displaystyle \mathbf {\mathcal {D}} _{\mu }=\mathbf

Tau function (integrable systems) (6,256 words) [view diff] exact match in snippet view article

n{\displaystyle \{\alpha _{i}\}_{i=1,\dots ,n}} corresponding to the rational covariant derivative operator ∂∂z−∑i=1nNiz−αi{\displaystyle {\partial \over \partial z}-\sum