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تسجيل مستخدم جديدSU(2) Symmetry and Conservation of Helicity for a Dirac Particle in a Static Magnetic Field at First Order
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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 $mathbf{k}=mathbf{p_f}+mathbf{p_i}$, the momentum transfer $mathbf{q}=mathbf{p_f-p_i}$, and $mathbf{l}=mathbf{ktimes q}$. 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 $mathbf{k}$, and the flipping of its component along $mathbf{q}$, 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.
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