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


Shikakhwa M. S. , Albaid A.

REVISTA MEXICANA DE FISICA, cilt.63, ss.474-480, 2017 (SCI İndekslerine Giren Dergi) identifier

  • Cilt numarası: 63 Konu: 5
  • Basım Tarihi: 2017
  • Dergi Adı: REVISTA MEXICANA DE FISICA
  • Sayfa Sayıları: ss.474-480

Özet

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 1 = k x 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.