Causal fermion systems are constructed for globally hyperbolic spacetimes such that their continuum limit satisfies the Euler-Lagrange equations of the causal action principle if and only if the coupled Einstein-Dirac equations hold.
Light-Cone Expansion of the Dirac Sea in the Presence of Chiral and Scalar Potentials
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abstract
We study the Dirac sea in the presence of external chiral and scalar/pseudoscalar potentials. In preparation, a method is developed for calculating the advanced and retarded Green's functions in an expansion around the light cone. For this, we first expand all Feynman diagrams and then explicitly sum up the perturbation series. The light-cone expansion expresses the Green's functions as an infinite sum of line integrals over the external potential and its partial derivatives. The Dirac sea is decomposed into a causal and a non-causal contribution. The causal contribution has a light-cone expansion which is closely related to the light-cone expansion of the Green's functions; it describes the singular behavior of the Dirac sea in terms of nested line integrals along the light cone. The non-causal contribution, on the other hand, is, to every order in perturbation theory, a smooth function in position space.
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math-ph 2years
2026 2representative citing papers
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.
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The Continuum Limit Analysis of Causal Fermion Systems for Curved Spacetimes
Causal fermion systems are constructed for globally hyperbolic spacetimes such that their continuum limit satisfies the Euler-Lagrange equations of the causal action principle if and only if the coupled Einstein-Dirac equations hold.
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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.