On the Fock space for nonrelativistic anyon fields and braided tensor products

Gerald A. Goldin, Shahn Majid

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

Abstract

We realize the physical N-anyon Hilbert spaces, introduced previously via unitary representations of the group of diffeomorphisms of the plane, as N-fold braided-symmetric tensor products of the 1-particle Hilbert space. This perspective provides a convenient Fock space construction for nonrelativistic anyon quantum fields along the more usual lines of boson and fermion fields, but in a braided category, and clarifies how discrete (lattice) anyon fields relate to anyon fields in the continuum. We also see how essential physical information is encoded. In particular, we show how the algebraic structure of the anyonic Fock space leads to a natural anyonic exclusion principle related to intermediate occupation number statistics, and obtain the partition function for an idealized gas of fixed anyonic vortices.

Original languageEnglish (US)
Pages (from-to)3770-3787
Number of pages18
JournalJournal of Mathematical Physics
Volume45
Issue number10
DOIs
StatePublished - Oct 2004

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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