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arXiv:hep-th/0405207 · International Journal of Theoretical Physics

Dirac Particle in an Aharonov-Bohm Potential: The Structure of the First Order S-matrix

M. S. Shikakhwa

Published Jan 9, 2007• 5 citations
arXivHTMLPDF
DOI
10.1007/s10773-006-9246-5

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For a Dirac particle in an Aharonov-Bohm (AB) potential, it is shown that the spin interaction (SI) operator which governs the transitions in the spin sector of the first order S-matrix closes the SO(3) algebra with other two operators in the spin space of the particle. Expressing the helicity operators of the incident and scattered particles in terms of these new generators, conservation of helicity in the transition is established algebraically as a consequence of this algebra at the operator level in a simple and transparent manner. The case of a non-relativistic spin-1/2 particle is also discussed along similar lines.
A partial wave analysis using the basis of the total angular momentum operator J3{J}_{3}J3​ is carried out for the first order Born amplitude of a Dirac particle in an Aharonov-Bohm potential. It is demonstrated that the s partial wave contributes to the scattering amplitude in contrast with the case with scalar nonrelativistic particles. We suggest that this explains the fact that the first order Born amplitude of a Dirac particle coincides with the exact amplitude expanded to the same order, where it does not for a scalar particle. An interesting algebra involving the Dirac velocity operator and the angular observables is discovered and its consequences are exploited.