Chiral Spin Noncommutative Space and Anomalous Dipole Moments

TL;DR

This paper develops a chiral spin noncommutative space model, deriving gauge theories and identifying corrections that influence matter field currents and dipole moments, with experimental bounds applied to muons.

Contribution

It introduces a novel chiral spin noncommutative space framework with gauge theory formulation and analyzes its physical implications, including anomalous dipole moments.

Findings

Noncommutative corrections affect matter and gauge field equations.

Corrections include contributions to Noether current and dipole moments.

Experimental bounds on noncommutative parameters are established for muons.

Abstract

We introduce a new model of spin noncommutative space in which noncommutative extension of the coordinate operators are assumed to be chirality dependent. Noncommutative correspondences of classical fields are defined via Weyl ordering, and the maps are represented by a spin-dependent translation operator. Based on the maps, gauge field theory in chiral spin noncommutative space is established. The corresponding gauge transformations are induced by a local phase rotation on commutative functions, and hence are consistent with the ordinary gauge transformations by definition. Furthermore, a general extension of the ordering between Dirac matrix and gauge potential is introduced. Noncommutative corrections on equations of motion of matter and gauge fields are studied. We find that there are two kinds of corrections. The first kind of correction involves derivatives of the matter field, and hence contribute the ordinary Noether current. On the other hand, the second kind of correction depends only on derivatives of the gauge fields, and hence contribute anomalous magnetic and electric dipole moments of the matter field. Moreover, experimental bounds on the noncommutative parameters for muon lepton are studied in a simplified model.