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. IvanovAtominstitut der Österreichischen Universitäten, Arbeitsbereich Kernphysik und Nukleare Astrophysik, Technische Universität Wien, Wiedner Hauptstrasse 8-10, 1040 Wien, Österreich faber@kph.tuwien.ac.at
(Received: 16 December 2000 / Revised version: 23 April 2001 / Published online: 13 June 2001 -© Springer-Verlag / Società Italiana di Fisica 2001)
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.
© Società Italiana di Fisica, Springer-Verlag 2001
