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 language||English (US)|
|Number of pages||5|
|Journal||Journal of Mathematical Physics|
|Publication status||Published - Dec 1 1980|
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics