Spin-Statistics and CPT Theorems in Noncommutative Field Theory

TL;DR

This paper demonstrates that the fundamental spin-statistics relation and CPT symmetry largely hold in noncommutative quantum field theories, despite some symmetry violations and nonlocal effects.

Contribution

It proves the validity of the spin-statistics relation and CPT theorem in noncommutative QFT, highlighting conditions where symmetries are broken or preserved.

Findings

Spin-statistics relation remains valid in NC QFT.

CPT theorem holds despite nonlocality and Lorentz violation.

Certain noncommutative cases break individual symmetries C, T, P.

Abstract

We show that Pauli's spin-statistics relation remains valid in noncommutative quantum field theories (NC QFT), with the exception of some peculiar cases of noncommutativity between space and time. We also prove that, while the individual symmetries C and T, and in some cases also P, are broken, the CPT theorem still holds in general for noncommutative field theories, in spite of the inherent nonlocality and violation of Lorentz invariance.