Classical limit for the scattering of Dirac particles in a magnetic field

DOI10.1088/0305-4470/36/10/314zbMATH Open1027.81032arXivquant-ph/0211195OpenAlexW3098317895MaRDI QIDQ4807140

Author name not available (Why is that?)

Publication date: 21 December 2003

Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)

Abstract: We present a relativistic quantum calculation at first order in perturbation theory of the differential cross section for a Dirac particle scattered by a solenoidal magnetic field. The resulting cross section is symmetric in the scattering angle as those obtained by Aharonov and Bohm (AB) in the string limit and by Landau and Lifshitz (LL) for the non relativistic case. We show that taking pr_0|sin( heta/2)|/hbar<<1 in our expression of the differential cross section it reduces to the one reported by AB, and if additionally we assume heta << 1 our result becomes the one obtained by LL. However, these limits are explicitly singular in hbar as opposed to our initial result. We analyze the singular behavior in hbar and show that the perturbative Planck's limit (hbar -> 0) is consistent, contrarily to those of the AB and LL expressions. We also discuss the scattering in a uniform and constant magnetic field, which resembles some features of QCD.

Full work available at URL: https://arxiv.org/abs/quant-ph/0211195

zbMATH Keywords

Aharonov-Bohm effect classical limit quantum scattering Dirac particle first order perturbation scattering angle solenoidal magnetic field

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Perturbation theories for operators and differential equations in quantum theory (81Q15) Special relativity (83A05) (2)-body potential quantum scattering theory (81U05) Singular perturbations, turning point theory, WKB methods for ordinary differential equations (34E20)