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 to First Order in the External Potential
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abstract
The perturbation of the Dirac sea to first order in the external potential is calculated in an expansion around the light cone. It is shown that the perturbation consists of a causal contribution, which describes the singular behavior of the Dirac sea on the light cone and contains bounded line integrals over the potential and its partial derivatives, and a non-causal contribution, which is a smooth function. As a preparatory step, we construct a formal solution of the inhomogeneous Klein-Gordon equation in terms of an infinite series of line integrals. More generally, the method presented can be used for an explicit analysis of Feynman diagrams of the Dirac, Klein-Gordon, and wave equations in position space.
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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.