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.
Quantization of Maxwell's equations on curved backgrounds and general local covariance
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abstract
We develop a quantization scheme for Maxwell's equations without source on an arbitrary four dimensional globally hyperbolic spacetime. The field strength tensor is the key dynamical object and it is not assumed a priori that it descends from a vector potential. It is shown that, in general, the associated field algebra can contain a non trivial centre and, on account of this, such a theory cannot be described within the framework of general local covariance unless further restrictive assumptions on the topology of the spacetime are made.
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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.