SU(2) symmetry and conservation of helicity for a Dirac particle in a static magnetic field at first order
Revista Mexicana de Fisica, cilt.63, sa.5, ss.474-480, 2014 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 63 Sayı: 5
- Basım Tarihi: 2014
- Dergi Adı: Revista Mexicana de Fisica
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.474-480
- Anahtar Kelimeler: Dirac equation, Helicity conservation, S-matrix, Scattering
- TED Üniversitesi Adresli: Hayır
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 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.