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Bosonization and generalized Mandelstam soliton operators. (English) Zbl 1191.81151
Summary: The generalized massive Thirring model (GMT) with three fermion species is bosonized in the context of the functional integral and operator formulations and shown to be equivalent to a generalized sine-Gordon model (GSG) with three interacting soliton species. The generalized Mandelstam soliton operators are constructed and the fermion-boson mapping is established through a set of generalized bosonization rules in a quotient positive-definite Hilbert space of states. Each fermion species is mapped to its corresponding soliton in the spirit of particle/soliton duality of Abelian bosonization. In the semi-classical limit one recovers the so-called $$SU(3)$$ affine Toda model coupled to matter fields (ATM) from which the classical GSG and GMT models were recently derived in the literature. The intermediate ATM-like effective action possesses some spinors resembling the higher grading fields of the ATM theory which have non-zero chirality. These fields are shown to disappear from the physical spectrum, thus providing a bag-model-like confinement mechanism and leading to the appearance of massive fermions (solitons). The ordinary MT/SG duality turns out to be related to each $$SU(2)$$ sub-group. The higher rank Lie algebra extension is also discussed.
##### MSC:
 81T10 Model quantum field theories
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