Non-Abelian bosonization in two dimensions. (English) Zbl 0536.58012

One of the most startling aspects of mathematical physics in \(1+1\) dimensions is the existence of a non-local transformation from local Fermi fields to local Bose fields. This fact is remarkably useful for elucidating the properties of a \(1+1\) dimensional theories. Many phenomena that are difficult to understand in the Fermi language have a simple semiclassical explanation in the Bose formalism. A major limitation of the usual bosonization procedure is that in the case of Fermi theories with non-Abelian symmetries, these symmetries are not preserved by the bosonization. In this paper the author gives a non-Abelian generalization of the usual formulas for bosonization of fermions in \(1+1\) dimensions which manifestly possess all the symmetries of the Fermi theory.
Reviewer: M.Martellini


81S10 Geometry and quantization, symplectic methods
53D50 Geometric quantization
81T60 Supersymmetric field theories in quantum mechanics
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