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

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 $\mathbfΣ$ along the direction of the total momentum of the system, and the two operators constructed from the projections of the $\mathbfΣ$ 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 .