### 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 ℝ^{s}. 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 ℝ^{s}. The vector potential plays no role in this description of the Aharonov-Bohm effect.

Original language | English (US) |
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Pages (from-to) | 1664-1668 |

Number of pages | 5 |

Journal | Journal of Mathematical Physics |

Volume | 22 |

Issue number | 8 |

Publication status | Published - Dec 1 1980 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Mathematical Physics*,

*22*(8), 1664-1668.