Maxwell's equations in nLab
for the Lie derivative of differential forms along v 5 v^5 , and make use of Cartan's magic formula expressing it as an anti-commutator, as ...
Chen Ning Yang, The conceptual origins of Maxwell's equations and gauge theory, Phyics Today 67 11 (2014) [doi:10.1063/PT.3.2585, pdf].
3. References. General. See most references on electromagnetism, e.g. these articles. G. Russakoff, A Derivation of the Macroscopic Maxwell Equations, American ...
The Yang-Mills equations are the equations of motion/Euler-Lagrange equations of Yang-Mills theory. They generalize Maxwell's equations.
higher category theory and physics in nLab
... Maxwell's equations imply that at the support of any magnetic charge the 2-form representing the field strength of the electromagnetic field ...
geometry of physics -- perturbative quantum field theory in nLab
ϕ * ω = ϕ * ( ω i d x i ) ≔ ( ϕ * ω ) i ∂ ϕ i ∂ x ˜ j d x ˜ j = ( ω i ∘ ϕ ) ⋅ ∂ ϕ i ∂ x ˜ j d x ˜ j .
Nevertheless, Kirchhoff's laws preserve the cohomological nature of Maxwell's equations: where the latter involves de Rham cohomology and hence ...
On formulating classical electromagnetism and especially Maxwell's equations in terms of differential forms and the Hodge star operator:.
... Maxwell's equations have no charge sources anywhere, and still effectively look to an observer constrained to one of the two Minkowski ...
Chen Ning Yang, The conceptual origins of Maxwell's equations and gauge theory, Phyics Today 67 11 (2014) [doi:10.1063/PT.3.2585, pdf].
geometry of physics -- flux quantization in nLab
3. Flux/Charge quantization laws ... With the solution space (Prop. 2.15) of higher Maxwell-type equations of motion (Def. 2.7) in hand, the ...
On the historical origin of Maxwell's equations, the “vector potential” and (Yang-Mills) gauge theory: A. C. T. Wu, Chen Ning Yang ...
A first idea of quantum field theory -- Lagrangians in nLab
These PDEs are called the vacuum Maxwell's equations. This, too, is a free field theory according to def. 1.25. Example 1.30. (equation of ...
This is familiar from, say, Maxwell's equations, where such a J J appears on the right hand side as the electromagnetic source form. d ⋆ F ...
Chen Ning Yang, The conceptual origins of Maxwell's equations and gauge theory, Phyics Today 67 11 (2014) [doi:10.1063/PT.3.2585, pdf].
geometry of physics -- G-structure and Cartan geometry in nLab
example: the other 2 Maxwell equations: d ⋆ F = j el \mathbf{d} \star F = j_{el} . Einstein-Maxwell theory. Almost complex structure. almost ...
Euler-Lagrange equation in nLab
3. Examples · The Euler-Lagrange equations of the Einstein-Hilbert action are Einstein's equations of gravity. · Maxwell's equations · Yang-Mills ...
Thus, the Yang-Mills equations reduce to Maxwell's equations for an electromagnetic field on M M : ... equation which upon iteration yields the ...
Steven Weinberg, Photons and Gravitons in Perturbation Theory: Derivation of Maxwell's and Einstein's Equations,” Phys. Rev. 138 (1965) B988 ...
Higher gauge theories of Maxwell type · the system of Bianchi identity differential equations (cf. at Gauss law). (1) d F → = P → ( F → ) \mathrm ...