QED in external fields from the spin representation

Details QED in external fields from the spin representation QED in external fields from the spin representation

1994-02-16

arxiv.org/abs/hep-th/9402098v1

J.Math.Phys.35:3340-3367,1994

Physics

High Energy Physics

High Energy Physics - Theory

32 pages, Plain TeX, UCR-FM-01-94

Scientific paper

10.1063/1.530472

Systematic use of the infinite-dimensional spin representation simplifies and rigorizes several questions in Quantum Field Theory. This representation permutes ``Gaussian'' elements in the fermion Fock space, and is necessarily projective: we compute its cocycle at the group level, and obtain Schwinger terms and anomalies from infinitesimal versions of this cocycle. Quantization, in this framework, depends on the choice of the ``right'' complex structure on the space of solutions of the Dirac equation. We show how the spin representation allows one to compute exactly the S-matrix for fermions in an external field; the cocycle yields a causality condition needed to determine the phase.

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