PCT, spin and statistics, and analytic wave front set

TL;DR

This paper introduces a generalized derivation of the spin-statistics and PCT theorems using the analytic wave front set, extending the results to nonlocal quantum fields with singular vacuum expectation values.

Contribution

It presents a novel approach that covers nonlocal quantum fields by employing the analytic wave front set, replacing local commutativity with an asymptotic condition.

Findings

Generalized derivation of spin-statistics and PCT theorems

Applicable to nonlocal quantum fields with singular vacuum states

Replaces microcausality with asymptotic commutativity

Abstract

A new, more general derivation of the spin-statistics and PCT theorems is presented. It uses the notion of the analytic wave front set of (ultra)distributions and, in contrast to the usual approach, covers nonlocal quantum fields. The fields are defined as generalized functions with test functions of compact support in momentum space. The vacuum expectation values are thereby admitted to be arbitrarily singular in their space-time dependence. The local commutativity condition is replaced by an asymptotic commutativity condition, which develops generalizations of the microcausality axiom previously proposed.