Hidden symmetries in two dimensional field theory

  • Creutz M
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Abstract

The bosonization process elegantly shows the equivalence of massless scalar and fermion fields in two space-time dimensions. However, with multiple fermions the technique often obscures global symmetries. Witten's non-Abelian bosonization makes these symmetries explicit, but at the expense of a somewhat complicated bosonic action. Frenkel and Kac have presented an intricate mathematical formalism relating the various approaches. Here, I reduce these arguments to the simplest case of a single massless scalar field. In particular, using only elementary quantum field theory concepts, I expose a hidden SU (2) × SU (2) chiral symmetry in this trivial theory. I then discuss in what sense this field should be interpreted as a Goldstone boson. © 2006 Elsevier Inc. All rights reserved.

Author-supplied keywords

  • Bosonization
  • Chiral symmetry
  • Goldstone bosons

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Authors

  • Michael Creutz

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