Wick rotation for quantum field theories on degenerate Moyal space(-time)

TL;DR

This paper establishes a framework connecting Euclidean and Minkowski quantum field theories on Moyal space, demonstrating that Wick rotation and deformation processes commute, thus advancing understanding of noncommutative quantum field theories.

Contribution

It introduces a general correspondence between Euclidean and Minkowski quantum field theories on Moyal space, showing that Wick rotation and deformation commute within this framework.

Findings

Wick rotation can be extended to Moyal space(-time) with time remaining commutative.

Deformation via Rieffel and warped convolution fits into the Wick rotation framework.

Wick rotation and deformation processes commute in this setting.

Abstract

In this paper the connection between quantum field theories on flat noncommutative space(-times) in Euclidean and Lorentzian signature is studied for the case that time is still commutative. By making use of the algebraic framework of quantum field theory and an analytic continuation of the symmetry groups which are compatible with the structure of Moyal space, a general correspondence between field theories on Euclidean space satisfying a time zero condition and quantum field theories on Moyal Minkowski space is presented ("Wick rotation"). It is then shown that field theories transferred to Moyal space(-time) by Rieffel deformation and warped convolution fit into this framework, and that the processes of Wick rotation and deformation commute.