Anticommutators and propagators of Moyal star-products for Dirac field on noncommutative spacetime

TL;DR

This paper investigates the behavior of Dirac fields on noncommutative spacetime using Moyal star-products, revealing that their propagators are identical to those in ordinary spacetime, which simplifies understanding quantum fields in noncommutative geometry.

Contribution

The study constructs Moyal star-product propagators for Dirac fields and demonstrates their equivalence to standard propagators in commutative spacetime, providing new insights into noncommutative quantum field theory.

Findings

Moyal anticommutators are computed for Dirac fields.

Propagators of Moyal star-products match those in commutative spacetime.

Results simplify the analysis of quantum fields on noncommutative spacetime.

Abstract

We study the Moyal anticommutators and their expectation values between vacuum states and non-vacuum states for Dirac fields on noncommutative spacetime. Then we construct the propagators of Moyal star-products for Dirac fields on noncommutative spacetime. We find that the propagators of Moyal star-products for Dirac fields are equal to the propagators of Dirac fields on ordinary commutative spacetime.