Chiral Spin Noncommutative Space and Anomalous Dipole Moments

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.

Covariant version of the Pauli Hamiltonian, spin-induced noncommutativity, Thomas precession, and the precession of spin

“…In this regard, we point out that spinning particles represent an exceptional example of intrinsically noncommutative and relativistic-invariant theory, with the spin-induced noncommutativity that manifests itself already at the Compton scale. The effects due to noncommutative geometry are of considerable interest in the current literature [46][47][48][49][50][51][52][53][54], and certainly deserve a detailed study in the relativistic-invariant context of spin-induced noncommutativity.…”

“…Using Eqs. ( 53) and ( 11) in (51), we obtain the expression that can be thought as an equation of motion of spin axis in the comoving frame…”