SU(2) SYMMETRY AND CONSERVATION OF HELICITY FOR A DIRAC PARTICLE IN A STATIC MAGNETIC FIELD AT FIRST ORDER

摘要

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