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

• M. S. Shikakhwa ^[1] ; A. Albaid ^[2]
  1. [1] University of Jordan, Turkey
  2. [2] Oklahoma Sate University, OK, USA
• Localización: Revista Mexicana de Física, ISSN-e 0035-001X, Vol. 63, Nº. 5, 2017, págs. 474-480
• Idioma: inglés
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• Resumen

  • 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 = p_(f) + p_(i), the momentum transfer q = p_(f) + p_(i), 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.