On the Fisk-Tait Equation for Spin-3/2 Fermions Interacting With an External Magnetic Field in Noncommutative Space-Time

TL;DR

This paper explores the Fisk-Tait equation for spin-3/2 fermions in noncommutative space-time, analyzing the effects of noncommutativity on current density, charge, and spin properties, with implications for fermion-boson interactions.

Contribution

It introduces a detailed study of the Fisk-Tait equation in noncommutative space-time, including continuity equations and spin current densities, using the Moyal-Weyl product and Holstein-Primakoff transformation.

Findings

Space-time noncommutativity affects current density and spin properties.

Total charge remains indefinite despite noncommutativity.

Linking fermions and bosons via Fock space is analyzed.

Abstract

In this paper, we investigated the Fisk-Tait equation in interaction with an external magnetic field in noncommutative space-time. Knowing that the space-time noncommutativity is introduced through the Moyal-Weyl product known method. Consequently, we studied the continuity equation in both commutative and noncommutative space-time; there we examined the influence of the space-time noncommutativity on the current density quadri-vector. Moreover, we find that the total charge obtained from the probability density still indefinite even when space does not commute. Furthermore, we found the spin current density in the two different spin directions. We also investigated the linking between the fermions and the bosons in the Fock space using the Holstein-Primakoff transformation.