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

2017-09-01
Shikakhwa, M. S.
Albaid, A.
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.

Citation Formats
M. S. Shikakhwa and A. Albaid, “SU(2) symmetry and conservation of helicity for a Dirac particle in a static magnetic field at first order,” REVISTA MEXICANA DE FISICA, vol. 63, no. 5, pp. 474–480, 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/65396.