nLab
Einstein-Yang-Mills 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-Yang-Mills theory in physics is the theory/model (in theoretical physics) describing gravity together with Yang-Mills fields such as the electroweak field or the strong nuclear force of quantum chromodynamics. For the special case that the gauge group is the circle group this reproduces Einstein-Maxwell theory.

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

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

where

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+(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

Revised on March 2, 2014 16:10:20 by Aistis Raulinaitis? (12.227.104.109)