2004/09/25 by Harold Blas, Blas, Harold · 1 citation
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Quantum Chromodynamics and Particle Interactions #Quantum Mechanics and Non-Hermitian Physics #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/0409269
29 pages, LaTex. Based on paper hep-th/0404058. Higher rank Lie algebra discussion added. Invited paper for "Progress in Boson Research" (Nova Science Publishers)
arxiv created 2004/09/25 · arxiv updated 2009/12/01
The generalized massive Thirring model (GMT) with Nf[=number of positive roots of su(n)] 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 Nf interacting soliton species. The generalized Mandelstam-Halpern 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(n) 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 the massive fermions (solitons). The su(3) and su(4) cases are discussed in detail.