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

searching for Covariant derivative 43 found (284 total)

alternate case: covariant derivative

Yang–Mills–Higgs equations (468 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 (3,338 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 (370 words) [view diff] exact match in snippet view article find links to article

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

Spin connection (2,944 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 ∂ ; μ e ν b {\displaystyle \partial _{;\mu }e^{\nu b}} of the contravariant

Komar superpotential (393 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

Normal coordinates (1,327 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 (1,683 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

Metric-affine gravitation theory (1,253 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

Tetradic Palatini action (4,657 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 D α V I = ∂ α V I + ω α I J V J . {\displaystyle

Higgs mechanism (6,691 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 (1,308 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

Scalar electrodynamics (963 words) [view diff] exact match in snippet view article find links to article

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

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.

Vanishing scalar invariant spacetime (363 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

Fermi–Walker transport (894 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

Newton–Cartan theory (1,414 words) [view diff] exact match in snippet view article find links to article

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

Dirac equation (13,081 words) [view diff] exact match in snippet view article find links to article

scalar electrodynamics: the partial derivative is promoted to a covariant derivative D μ {\displaystyle D_{\mu }} D μ ψ = ∂ μ ψ + i e A μ ψ , {\displaystyle

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

Optical scalars (2,874 words) [view diff] exact match in snippet view article find links to article

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

Supersymmetric gauge theory (1,618 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 D M = d M + i q A M {\displaystyle D_{M}=d_{M}+iqA_{M}}

Diamagnetism (2,404 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 Küstler, Gerald (2007). "Diamagnetic Levitation – Historical Milestones"

Spacetime symmetries (1,519 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 Noether's

Hessian matrix (3,537 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 (2,251 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

Supermultiplet (2,075 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 ˙ − i θ α σ α α ˙ μ

Komar mass (2,245 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: a b = ∇ u u b = u c

Tensor software (2,065 words) [view diff] exact match in snippet view article find links to article

multiplication by scalar, trace, contraction, partial derivative, covariant derivative, and permutation of indices, and provides facilities for calculating

Bogomol'nyi–Prasad–Sommerfield bound (2,633 words) [view diff] exact match in snippet view article find links to article

is the field strength tensor, D μ {\displaystyle D_{\mu }} is the covariant derivative, ϕ a {\displaystyle \phi ^{a}} is the Higgs field in the adjoint

Fréchet space (5,039 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 D j s . {\displaystyle D^{j}s.} Then ‖ s ‖ n = ∑ j = 0 n sup x

Harmonic coordinates (2,599 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 (3,252 words) [view diff] exact match in snippet view article find links to article

In this expression, D μ {\displaystyle D_{\mu }{\Big .}} is the covariant derivative, B μ ν = D μ B ν − D ν B μ {\displaystyle B_{\mu \nu }=D_{\mu }B_{\nu

Glossary of string theory (5,167 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 (2,349 words) [view diff] exact match in snippet view article find links to article

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

Holonomy (5,901 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 (7,325 words) [view diff] exact match in snippet view article find links to article

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

Vasiliev equations (9,794 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 − ϖ α β ( y α ∂ ∂ y β + y β ∂ ∂ y α ) − . . . {\displaystyle

Loop quantum gravity (16,616 words) [view diff] exact match in snippet view article find links to article

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

Hamiltonian constraint of LQG (7,798 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, ∇ a ψ = ( ∂ a − i 4 ω a I J

De Broglie–Bohm theory (16,716 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

Majorana equation (8,807 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

Loop representation in gauge theories and quantum gravity (5,585 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 D μ = I ∂ μ + i g A μ ( x ) {\displaystyle \mathbf {\mathcal {D}}

Tau function (integrable systems) (6,689 words) [view diff] exact match in snippet view article

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