nLab Einstein-Maxwell theory




Differential cohomology


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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 \,,


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

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+(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)


Section Prequantum gauge theory and Gravity in

See also

Last revised on May 4, 2020 at 10:43:07. See the history of this page for a list of all contributions to it.