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Light-Cone Expansion of the Dirac Sea to First Order in the External Potential
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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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Cited by 2 Pith papers
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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...
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A Gauge Fixing Procedure for Causal Fermion Systems
A canonical gauge fixing for causal fermion systems is constructed via symmetric and Gaussian wave charts, fixing local gauge freedom up to global transformations.
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