Conservation of Helicity and SU(2) Symmetry in First Order Scattering

TL;DR

This paper demonstrates that helicity conservation in first order elastic scattering of Dirac particles enforces a specific spin interaction structure that exhibits SU(2) symmetry and depends on intrinsic axes defined by scattering geometry.

Contribution

It reveals that helicity conservation determines a universal form of the spin interaction operator with SU(2) symmetry in first order scattering.

Findings

Helicity conservation constrains the spin interaction operator form.

The spin interaction operator forms an SU(2) algebra with other operators.

Intrinsic axes defined by scattering geometry act as symmetry axes.

Abstract

The structure of the spin interaction operator (SI) (the interaction that remains after space variables are integrated out) in the first order S-matrix element of the elastic scattering of a Dirac particle in a general helicity-conserving vector potential is investigated.It is shown that the conservation of helicity dictates a specific form of the SI regardless of the explicit form of the vector potential. This SI closes the SU(2) algebra with other two operators in the spin space of the particle. The directions of the momentum transfer vector and the vector bisecting the scattering angle seem to define some sort of "intrinsic" axes at this order that act as some symmetry axes for the whole spin dynamics . The conservation of helicity at this order can be formulated as the invariance of the component of the helicity of the particle along the bisector of the scattering angle in the transition.