Covariant quantization of field theories on T-Minkowski noncommutative spacetimes

TL;DR

This paper introduces a covariant quantization method for scalar fields on T-Minkowski noncommutative spacetimes, showing that key quantum functions remain identical to their commutative versions, thus avoiding IR/UV mixing issues.

Contribution

It develops a covariant quantization scheme for T-Minkowski noncommutative spacetimes and proves the equivalence of quantum functions to the commutative case, including for interacting theories.

Findings

Wightman functions equal to commutative counterparts

Wick theorem structurally similar to commutative QFT

Absence of IR/UV mixing effects in the models studied

Abstract

We develop a quantization scheme for the quantum theory of a real scalar field on a class of non-commutative spacetime models collectively known as T-Minkowski. Requiring the theory to be covariant under T-Poincar\'e transformations, we find that for a subclass of models the Wightmann functions are equal to their commutative counterparts, and we are able to prove a Wick theorem for Wightmann functions that is structurally equivalent to the one encountered in commutative QFT. For some of these models we further extend the result to Green functions and to N-point functions of interacting QFT, which we also find to be commutative, leaving no space for IR/UV mixing effects advocated in other approaches to noncommutative QFT.