nLab Einstein-Yang-Mills-Dirac theory




Differential cohomology


physics, mathematical physics, philosophy of physics

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theory (physics), model (physics)

experiment, measurement, computable physics



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:(e,,ψ) XR(e)vol(e)+ XF eF + X(ψ,D e,ψ), 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) \,,


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)


  • 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.