The Spin Interaction of a Dirac Particle in an Aharonov-Bohm Potential in First Order Scattering

TL;DR

This paper analyzes the spin interactions of a Dirac particle in an Aharonov-Bohm potential during first order scattering, revealing a SU(2) algebra structure and proposing a natural framework for spin dynamics and helicity conservation.

Contribution

It introduces a novel SU(2) algebra structure for spin operators in AB scattering and proposes a natural intrinsic direction framework for spin dynamics at first order.

Findings

Spin interaction operator relates to rotation generators in spin space.

Operators form an SU(2) algebra, indicating a structured spin dynamics.

Helicity conservation is interpreted using spin projections along intrinsic directions.

Abstract

For a Dirac particle in an Aharonov-Bohm (AB) potential, it is shown that the spin interaction (SI) operator which governs the transitions in the spin sector of the first order S-matrix is related to one of the generators of rotation in the spin space of the particle. This operator, which is given by the projection of the spin operator $\mathbf{\Sigma}$ along the direction of the total momentum of the system, and the two operators constructed from the projections of the $\mathbf{\Sigma}$ operator along the momentum transfer and the z-directions close the SU(2) algebra.It is suggested, then, that these two directions of the total momentum and the momentum transfer form some sort of natural intrinsic directions in terms of which the spin dynamics of the scattering process at first order can be formulated conveniently. A formulation and an interpretation of the conservation of helicity at first order using the spin projection operators along these directions is presented .