QED in external fields from the spin representation

TL;DR

This paper uses the infinite-dimensional spin representation to rigorously analyze quantum electrodynamics in external fields, enabling exact S-matrix calculations and clarifying anomalies and causality conditions.

Contribution

It introduces a systematic approach using the spin representation to compute the S-matrix and analyze anomalies in QED with external fields.

Findings

Exact S-matrix for fermions in external fields computed.

Cocycle yields Schwinger terms and anomalies.

Causality condition derived from the cocycle.

Abstract

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.