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Particles and Fields

Eur. Phys. J. C 20, 723-757 (2001)
DOI: 10.1007/s100520100694

On the equivalence between sine-Gordon model and Thirring model in the chirally broken phase of the Thirring model

M. Faber and A.N. Ivanov

Atominstitut der Österreichischen Universitäten, Arbeitsbereich Kernphysik und Nukleare Astrophysik, Technische Universität Wien, Wiedner Hauptstrasse 8-10, 1040 Wien, Österreich


(Received: 16 December 2000 / Revised version: 23 April 2001 / Published online: 13 June 2001 -© Springer-Verlag / Società Italiana di Fisica 2001)

We investigate the equivalence between Thirring model and sine-Gordon model in the chirally broken phase of the Thirring model. This is unlike all other available approaches where the fermion fields of the Thirring model were quantized in the chiral symmetric phase. In the path integral approach we show that the bosonized version of the massless Thirring model is described by a quantum field theory of a massless scalar field and exactly solvable, and the massive Thirring model bosonizes to the sine-Gordon model with a new relation between the coupling constants. We show that the non-perturbative vacuum of the chirally broken phase in the massless Thirring model can be described in complete analogy with the BCS ground state of superconductivity. The Mermin-Wagner theorem and Coleman's statement concerning the absence of Goldstone bosons in the 1+1-dimensional quantum field theories are discussed. We investigate the current algebra in the massless Thirring model and give a new value of the Schwinger term. We show that the topological current in the sine-Gordon model coincides with the Noether current responsible for the conservation of the fermion number in the Thirring model. This allows one to identify the topological charge in the sine-Gordon model with the fermion number.

© Società Italiana di Fisica, Springer-Verlag 2001