Bosonization in higher dimensions

C. P. Burgess, C. A. Lütken, F. Quevedo

Research output: Contribution to journalArticlepeer-review


Using the recently discovered connection between bosonization and duality transformations, we give an explicit path- integral representation for the bosonization of a massive fermion coupled to a U(1) gauge potential (such as electromagnetism) in d ≥ 2 space (D = d + 1 ≥ 3 spacetime) dimensions. We perform this integral explicitly in the limit of large fermion mass. We find that the bosonic theory is described by a rank d -1 antisymmetric Kalb-Ramond-type gauge potential, whose action is local for d = 2 (given by a Chern-Simons action), but nonlocal for d ≥ 3. By coupling to a statistical Chern-Simons field for d = 2, we obtain a bosonized formulation of anyons. The bosonic theory may be further dualized to a theory involving purely scalars, for any d, and we show this to be a higher-derivative theory for which the scalar decouples from the U(1) gauge potential.

Original languageEnglish (US)
Pages (from-to)18-24
Number of pages7
JournalPhysics Letters B
Issue number1
StatePublished - Sep 15 1994

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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