Light-Cone Expansion of the Dirac Sea to First Order in the External Potential

Details Light-Cone Expansion of the Dirac Sea to First Order in the External Potential Light-Cone Expansion of the Dirac Sea to First Order in the External Potential

1997-07-14

arxiv.org/abs/hep-th/9707128v4

Michigan Math.J. 46 (1999) 377-408

Physics

High Energy Physics

High Energy Physics - Theory

28 pages, typo in eq. (B.2) corrected

Scientific paper

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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