A limiting case of the causal action principle for causal fermion systems yields the Fock-space dynamics and Feynman diagrams of pQFT including non-abelian gauges and Dirac fields.
The global existence of Yang-Mills fields on curved space-times
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abstract
This is an introductory chapter in a series in which we take a systematic study of the Yang-Mills equations on curved space-times. In this first, we provide standard material that consists in writing the proof of the global existence of Yang-Mills fields on arbitrary curved space-times using the Klainerman-Rodnianski parametrix combined with suitable Gr\"onwall type inequalities. While the Chru\'sciel-Shatah argument requires a simultaneous control of the $L^{\infty}_{loc}$ and the $H^{2}_{loc}$ norms of the Yang-Mills curvature, we can get away by controlling only the $H^{1}_{loc}$ norm instead, and write a new gauge independent proof on arbitrary, fixed, sufficiently smooth, globally hyperbolic, curved 4-dimensional Lorentzian manifolds. This manuscript is written in an expository way in order to provide notes to Master's level students willing to learn mathematical General Relativity.
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The Fock Space Dynamics of Causal Fermion Systems: Non-Abelian Gauge Fields
A limiting case of the causal action principle for causal fermion systems yields the Fock-space dynamics and Feynman diagrams of pQFT including non-abelian gauges and Dirac fields.