On the equivalence between sine-Gordon model and Thirring model in the chirally broken phase of the Thirring model |
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Authors: | M Faber AN Ivanov |
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Institution: | Atominstitut der ?sterreichischen Universit?ten, Arbeitsbereich Kernphysik und Nukleare Astrophysik, Technische Universit?t Wien, Wiedner Hauptstrasse 8–10, 1040 Wien, ?sterreich, AT
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Abstract: | 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.
Received: 16 December 2000 / Revised version: 23 April 2001 / Published online: 13 June 2001 |
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