SU(2) symmetry and conservation of helicity for a Dirac particle in a static magnetic field at first order


Shikakhwa M., Albaid A.

Revista Mexicana de Fisica, vol.63, no.5, pp.474-480, 2014 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 63 Issue: 5
  • Publication Date: 2014
  • Journal Name: Revista Mexicana de Fisica
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.474-480
  • Keywords: Dirac equation, Helicity conservation, S-matrix, Scattering
  • TED University Affiliated: No

Abstract

We investigate the spin dynamics and the conservation of helicity in the first order S-matrix of a Dirac particle in any static magnetic field. We express the dynamical quantities using a coordinate system defined by the three mutually orthogonal vectors; the total momentum k = pf + pi, the momentum transfer q = pf - pi, and l = k × q. We show that this leads to an alternative symmetric description of the conservation of helicity in a static magnetic field at first order. In particular, we show that helicity conservation in the transition can be viewed as the invariance of the component of the spin along k and the flipping of its component along q, just as what happens to the momentum vector of a ball bouncing off a wall. We also derive a "plug and play" formula for the transition matrix element where the only reference to the specific field configuration, and the incident and outgoing momenta is through the kinematical factors multiplying a general matrix element that is independent of the specific vector potential present.