Infrared cutoffs and the adiabatic limit in noncommutative spacetime

TL;DR

This paper explores how to properly implement infrared cutoffs and their adiabatic limits in noncommutative Minkowski space quantum field theories, demonstrating the existence and consistency of the two-point function in this setting.

Contribution

It introduces a method for defining infrared cutoffs and establishing the adiabatic limit in noncommutative spacetime, extending techniques from commutative quantum field theory.

Findings

Infrared cutoff can be defined similarly to the commutative case.

The adiabatic limit of the two-point function exists.

The two-point function coincides with the expected value to all orders.

Abstract

We discuss appropriate infrared cutoffs and their adiabatic limit for field theories on the noncommutative Minkowski space in the Yang-Feldman formalism. In order to do this, we consider a mass term as interaction term. We show that an infrared cutoff can be defined quite analogously to the commutative case and that the adiabatic limit of the two-point function exists and coincides with the expectation, to all orders.