Representations of a local current algebra in nonsimply connected space and the Aharonov-Bohm effect

G. A. Goldin, R. Menikoff, D. H. Sharp

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Abstract

A recent paper established technical conditions for the construction of a class of induced representations of the nonrelativistic current group ℐ Λ script K, where of is Schwartz's space of rapidly decreasing C functions, and script K is a group of C∞ diffeomorphisms of ℝs. Bose and Fermi N-particle systems were recovered as unitarily inequivalent induced representations of the group by lifting the action of script K on an orbit Δ⊆ℐ' to its universal covering space Δ̃. For s≥3, Δ̃ is the coordinate space for N particles, which is simply connected. In two-dimensional space, however, the coordinate space is multiply connected, implying induced representations other than those describing the usual Bose or Fermi statistics; these are explored in the present paper. Likewise the Aharonov-Bohm effect is described by means of induced representations of the local observables, defined in a nonsimply connected region of ℝs. The vector potential plays no role in this description of the Aharonov-Bohm effect.

Original languageEnglish (US)
Pages (from-to)1664-1668
Number of pages5
JournalJournal of Mathematical Physics
Volume22
Issue number8
Publication statusPublished - Dec 1 1980

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All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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