A New Derivation of the CPT and Spin-Statistics Theorems in Non-Commutative Field Theories

TL;DR

This paper introduces an alternative axiomatic framework for non-commutative quantum field theories, demonstrating that CPT and Spin-Statistics theorems remain valid despite nonlocality, using asymptotic commutativity.

Contribution

It develops a new axiomatic approach based on asymptotic commutativity, ensuring CPT and Spin-Statistics theorems hold in non-commutative field theories with space-space non-commutativity.

Findings

Asymptotic commutativity replaces local commutativity in NCFT.

CPT and Spin-Statistics theorems are valid despite nonlocality.

Framework applies to scalar fields with space-space non-commutativity.

Abstract

We propose an alternative axiomatic description for non-commutative field theories (NCFT) based on some ideas by Soloviev to nonlocal quantum fields. The local commutativity axiom is replaced by the weaker condition that the fields commute at sufficiently large spatial separations, called asymptotic commutativity, formulated in terms of the theory of analytic functionals. The question of a possible violation of the CPT and Spin-Statistics theorems caused by nonlocality of the commutation relations $[\hat{x}_\mu,\hat{x}_\nu]=i\theta_{\mu\nu}$ is investigated. In spite of this inherent nonlocality, we show that the modification aforementioned is sufficient to ensure the validity of these theorems for NCFT. We restrict ourselves to the simplest model of a scalar field in the case of only space-space non-commutativity.