Noncommutative deformations of quantum field theories, locality, and causality

TL;DR

This paper explores noncommutative deformations of quantum field theories, focusing on locality, causality, and the mathematical structure of star products, proposing a new notion called θ-locality as an alternative to microcausality.

Contribution

It introduces the concept of θ-locality for noncommutative quantum fields and analyzes the structural properties of star products and their convergence, providing a framework for noncommutative QFT.

Findings

Defined the algebra suitable for Moyal and Wick-Voros products

Introduced θ-locality as an alternative to microcausality

Analyzed convergence and continuity conditions of star products

Abstract

We investigate noncommutative deformations of quantum field theories for different star products, particularly emphasizing the locality properties and the regularity of the deformed fields. Using functional analysis methods, we describe the basic structural features of the vacuum expectation values of star-modified products of fields and field commutators. As an alternative to microcausality, we introduce a notion of $\theta$-locality, where $\theta$ is the noncommutativity parameter. We also analyze the conditions for the convergence and continuity of star products and define the function algebra that is most suitable for the Moyal and Wick-Voros products. This algebra corresponds to the concept of strict deformation quantization and is a useful tool for constructing quantum field theories on a noncommutative space-time.