Commutators and propagators of Moyal star-products and microcausality for free scalar field on noncommutative spacetime

TL;DR

This paper investigates the properties of Moyal commutators and propagators in noncommutative scalar field theory, demonstrating microcausality preservation and constructing the associated Feynman propagator.

Contribution

It provides a detailed analysis of microcausality and constructs the Feynman propagator for free scalar fields on noncommutative spacetime, advancing understanding of quantum fields in noncommutative geometry.

Findings

Microcausality holds for linear operators of the free scalar field.

Moyal commutators' expectation values are computed for vacuum and non-vacuum states.

Constructed the Feynman propagator for noncommutative scalar field theory.

Abstract

We study the Moyal commutators and their expectation values between vacuum states and non-vacuum states for free scalar field on noncommutative spacetime. Then from the Moyal commutators, we find that the microcausality is satisfied for the linear operators of the free scalar field on noncommutative spacetime. We construct the Feynman propagator of Moyal star-product for noncommutative scalar field theory.