nLab
Einstein-Maxwell theory

Context

Gravity

Differential cohomology

Physics

physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes


theory (physics), model (physics)

experiment, measurement, computable physics

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.

standard model of particle physics and cosmology

theory:Einstein-Yang-Mills-Dirac-Higgs
gravityelectroweak and strong nuclear forcefermionic matterscalar field
field content:vielbein field eeprincipal connection \nablaspinor ψ\psiscalar field HH
Lagrangian:scalar curvature densityfield strength squaredDirac operator component densityfield strength 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+(λH 4μ 2H 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

Revised on January 14, 2013 18:20:59 by Urs Schreiber (203.116.137.162)