Reducible representations of CAR and CCR with possible applications to field quantization

TL;DR

This paper explores reducible representations of CAR and CCR in quantum field theory, demonstrating that they produce well-defined operators and could lead to finite quantum field theories, with applications to Dirac and Maxwell fields.

Contribution

It introduces a novel application of reducible CAR and CCR representations to second quantization, resulting in operators rather than distributions, potentially enabling finite quantum field theories.

Findings

Field operators are well-defined operators, not distributions

Formalism may lead to finite quantum field theories

Applications to Dirac and Maxwell fields

Abstract

Reducible representations of CAR and CCR are applied to second quantization of Dirac and Maxwell fields. The resulting field operators are indeed operators and not operator-valued distributions. Examples show that the formalism may lead to a finite quantum field theory.