Abstract

SHIKAKHWA, M.S.  and  ALBAID, A.. SU(2) symmetry and conservation of helicity for a Dirac particle in a static magnetic field at first order. Rev. mex. fis. [online]. 2017, vol.63, n.5, pp.474-480. ISSN 0035-001X.

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.

Keywords : S-matrix; scattering; Dirac equation; helicity conservation.

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