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

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.

The title is new, and the analysis in the manuscript has been made more precise. This revised version is to be published in J.Math.Phys

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• Ultrahyperfunctional Approach to Non-Commutative Quantum Field Theory
• Carrier cones of analytic functionals
• The Hierarchy Problem: From the Fundamentals to the Frontiers
• Energy renormalization and integrability within the massive neutrinos model