nLab
Einstein-Maxwell theory

Context

Gravity

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Formalism

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Definition

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Spacetime configurations

Properties

Spacetimes

vanishing positive
vanishing
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Quantum theory

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Differential cohomology

Ingredients

Connections on bundles

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Higher abelian differential cohomology

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Higher nonabelian differential cohomology

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Fiber integration

Application to gauge theory

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Physics

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Surveys, textbooks and lecture notes

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Contents

Idea

What is called Einstein-Maxwell theory in physics is the theory/model (in theoretical physics) describing gravity together with electromagnetism.

It is a local Lagrangian field theory defined by the action functional which is the Einstein-Hilbert action plus the Maxwell action functional? involving the given metric,

S G+EM:(e,) XR(e)vol(e)+ XF eF , S_{G+EM} \; \colon \; (e, \nabla) \mapsto \int_{X} R(e) vol(e) + \int_X F_\nabla \wedge \star_e F_\nabla \,,

where

This is the special case of Einstein-Yang-Mills theory for the gauge group being the circle group.

:---
and
content: ee \nabla ψ\psi HH
: density squared component density squared + potential density
L=L = R(e)vol(e)+R(e) vol(e) + F eF +\langle F_\nabla \wedge \star_e F_\nabla\rangle + (ψ,D (e,)ψ)vol(e)+ (\psi , D_{(e,\nabla)} \psi) vol(e) + H¯ eH+(λ|H| 4μ 2|H| 2)vol(e) \nabla \bar H \wedge \star_e \nabla H + \left(\lambda {\vert H\vert}^4 - \mu^2 {\vert H\vert}^2 \right) vol(e)

References

Section Prequantum gauge theory and Gravity in

See also

Last revised on December 7, 2015 at 08:14:51. See the history of this page for a list of all contributions to it.