Hidden symmetries in two dimensional field theory

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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.

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Creutz, M. (2006). Hidden symmetries in two dimensional field theory. Annals of Physics, 321(12), 2782–2792. https://doi.org/10.1016/j.aop.2006.01.003

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