Dirac particle in an Aharonov-Bohm potential: The structure of the first order S-matrix


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Shikakhwa M.

International Journal of Theoretical Physics, vol.46, no.2, pp.405-416, 2007 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 46 Issue: 2
  • Publication Date: 2007
  • Doi Number: 10.1007/s10773-006-9246-5
  • Journal Name: International Journal of Theoretical Physics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.405-416
  • Keywords: Aharonov-Bohm scattering, Scattering matrix
  • TED University Affiliated: No

Abstract

The structure of the interaction Hamiltonian in the first order S-matrix element of a Dirac particle in an Aharonov-Bohm (AB) field is analyzed and shown to have interesting interesting algebraic properties. It is demonstrated that as a consequence of these properties, this interaction Hamiltonian splits both the incident and outgoing waves in the the first order S-matrix into their Σ3/2-components (eigenstates of the third component of the spin). The matrix element can then be viewed as the sum of two transitions taking place in these two channels of the spin. At the level of partial waves, each partial wave of the conserved total angular momentum is split into two partial waves of the orbital angular momentum in a manner consistent with the conservation of the total angular momentum quantum number. © 2007 Springer Science+Business Media, LLC.