Schwinger functions in noncommutative quantum field theory

TL;DR

This paper investigates the properties of n-point functions in noncommutative quantum field theory, revealing their boundary value nature and explaining differences in renormalization between Minkowski and Euclidean frameworks.

Contribution

It demonstrates that scalar free fields' n-point functions are boundary values of analytic functions and clarifies why Euclidean and Minkowskian renormalizations differ.

Findings

n-point functions are boundary values of analytic functions

Euclidean approach does not connect directly unless time commutes

Renormalization differs between Minkowski and Euclidean regimes

Abstract

It is shown that the $n$-point functions of scalar massive free fields on the noncommutative Minkowski space are distributions which are boundary values of analytic functions. Contrary to what one might expect, this construction does not provide a connection to the popular traditional Euclidean approach to noncommutative field theory (unless the time variable is assumed to commute). Instead, one finds Schwinger functions with twistings involving only momenta that are on the mass-shell. This explains why renormalization in the traditional Euclidean noncommutative framework crudely differs from renormalization in the Minkowskian regime.