# nLab Einstein-Yang-Mills-Dirac theory

Contents

### Context

#### Gravity

gravity, supergravity

## Quantum theory

#### Differential cohomology

differential cohomology

# Contents

## Idea

What is called Einstein-Yang-Mills-Dirac theory in physics is the theory/model (in theoretical physics) describing gravity together with Yang-Mills fields and coupled to fermionic matter.

Einstein-Yang-Mills-Dirac 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,

$S_{G+YM} \; \colon \; (e, \nabla, \psi) \mapsto \int_{X} R(e) vol(e) + \int_X \langle F_\nabla \wedge \star_e F_\nabla\rangle + \int_X (\psi, D_{e,\nabla} \psi) \,,$

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 $e$principal connection $\nabla$spinor $\psi$scalar field $H$
Lagrangian:scalar curvature densityfield strength squaredDirac operator component densityfield strength squared + potential density
$L =$$R(e) vol(e) +$$\langle F_\nabla \wedge \star_e F_\nabla\rangle +$$(\psi , D_{(e,\nabla)} \psi) vol(e) +$$\nabla \bar H \wedge \star_e \nabla H + \left(\lambda {\vert H\vert}^4 - \mu^2 {\vert H\vert}^2 \right) vol(e)$

## References

• Gerd Rudolph, Torsten Tok, Igor P. Volobuev, Exact solutions in Einstein-Yang-Mills-Dirac systems, J.Math.Phys. 40 (1999) 5890-5904 (arXiv:gr-qc/9707060)

Section Prequantum gauge theory and Gravity in

Last revised on March 19, 2014 at 04:06:18. See the history of this page for a list of all contributions to it.