Finster, Felix and Grotz, Andreas (2010) The causal perturbation expansion revisited: Rescaling the interacting Dirac sea. JOURNAL OF MATHEMATICAL PHYSICS, 51 (7): 072301. ISSN 0022-2488, 1089-7658
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The causal perturbation expansion defines the Dirac sea in the presence of a time-dependent external field. It yields an operator whose image generalizes the vacuum solutions of negative energy and thus gives a canonical splitting of the solution space into two subspaces. After giving a self-contained introduction to the ideas and techniques, we show that this operator is, in general, not idempotent. We modify the standard construction by a rescaling procedure giving a projector on the generalized negative-energy subspace. The resulting rescaled causal perturbation expansion uniquely defines the fermionic projector in terms of a series of distributional solutions of Dirac equation. The technical core of the paper is to work out the combinatorics of the expansion in detail. It is also shown that the fermionic projector with interaction can be obtained from the free projector by a unitary transformation. We finally analyze the consequences of the rescaling procedure on the light-cone expansion. (C) 2010 American Institute of Physics. [doi:10.1063/1.3449058]
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | LIGHT-CONE EXPANSION; POLARIZED VACUUM; ELECTRONS; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Felix Finster |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 27 Jul 2020 11:50 |
| Last Modified: | 27 Jul 2020 11:50 |
| URI: | https://pred.uni-regensburg.de/id/eprint/24517 |
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