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Title: Two-dimensional thermofield bosonization

Abstract

The main objective of this paper was to obtain an operator realization for the bosonization of fermions in 1 + 1 dimensions, at finite, non-zero temperature T. This is achieved in the framework of the real-time formalism of Thermofield Dynamics. Formally, the results parallel those of the T = 0 case. The well-known two-dimensional Fermion-Boson correspondences at zero temperature are shown to hold also at finite temperature. To emphasize the usefulness of the operator realization for handling a large class of two-dimensional quantum field-theoretic problems, we contrast this global approach with the cumbersome calculation of the fermion-current two-point function in the imaginary-time formalism and real-time formalisms. The calculations also illustrate the very different ways in which the transmutation from Fermi-Dirac to Bose-Einstein statistics is realized.

Authors:
 [1];  [2];  [3]
  1. Instituto de Fisica, Universidade Federal Fluminense, Av. Litoranea S/N, Boa Viagem, Niteroi, CEP, 24210-340 Rio de Janeiro (Brazil). E-mail: rubens@if.uff.br
  2. Instituto de Fisica, Universidade Federal Fluminense, Av. Litoranea S/N, Boa Viagem, Niteroi, CEP, 24210-340 Rio de Janeiro (Brazil)
  3. Institut fuer Theoretische Physik, Universitaet Heidelberg, Philosophenweg 16, D-69120 Heidelberg (Germany)
Publication Date:
OSTI Identifier:
20766972
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics (New York); Journal Volume: 320; Journal Issue: 2; Other Information: DOI: 10.1016/j.aop.2005.07.003; PII: S0003-4916(05)00132-6; Copyright (c) 2005 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOSE-EINSTEIN STATISTICS; BOSON EXPANSION; FERMIONS; TRANSMUTATION; TWO-DIMENSIONAL CALCULATIONS

Citation Formats

Amaral, R.L.P.G., Belvedere, L.V., and Rothe, K.D. Two-dimensional thermofield bosonization. United States: N. p., 2005. Web. doi:10.1016/j.aop.2005.07.003.
Amaral, R.L.P.G., Belvedere, L.V., & Rothe, K.D. Two-dimensional thermofield bosonization. United States. doi:10.1016/j.aop.2005.07.003.
Amaral, R.L.P.G., Belvedere, L.V., and Rothe, K.D. Thu . "Two-dimensional thermofield bosonization". United States. doi:10.1016/j.aop.2005.07.003.
@article{osti_20766972,
title = {Two-dimensional thermofield bosonization},
author = {Amaral, R.L.P.G. and Belvedere, L.V. and Rothe, K.D.},
abstractNote = {The main objective of this paper was to obtain an operator realization for the bosonization of fermions in 1 + 1 dimensions, at finite, non-zero temperature T. This is achieved in the framework of the real-time formalism of Thermofield Dynamics. Formally, the results parallel those of the T = 0 case. The well-known two-dimensional Fermion-Boson correspondences at zero temperature are shown to hold also at finite temperature. To emphasize the usefulness of the operator realization for handling a large class of two-dimensional quantum field-theoretic problems, we contrast this global approach with the cumbersome calculation of the fermion-current two-point function in the imaginary-time formalism and real-time formalisms. The calculations also illustrate the very different ways in which the transmutation from Fermi-Dirac to Bose-Einstein statistics is realized.},
doi = {10.1016/j.aop.2005.07.003},
journal = {Annals of Physics (New York)},
number = 2,
volume = 320,
place = {United States},
year = {Thu Dec 15 00:00:00 EST 2005},
month = {Thu Dec 15 00:00:00 EST 2005}
}
  • We consider the perturbative computation of the N-point function of chiral densities of massive free fermions at finite temperature within the thermofield dynamics approach. The infinite series in the mass parameter for the N-point functions are computed in the fermionic formulation and compared with the corresponding perturbative series in the interaction parameter in the bosonized thermofield formulation. Thereby we establish in thermofield dynamics the formal equivalence of the massive free fermion theory with the sine-Gordon thermofield model for a particular value of the sine-Gordon parameter. We extend the thermofield bosonization to include the massive Thirring model.
  • We develop the construction of fermionic fields in terms of bosonic ones to describe free and interaction models in the circle, using thermofielddynamics. The description in the case of finite temperature is developed for both normal modes and zero modes. The treatment extends the thermofield-bosonization for periodic space.
  • We evaluate partition functions {ital Z}{sub {ital I}} in topologically nontrivial (instanton) gauge sectors in the bosonized version of the Schwinger model and in a gauged WZNW model corresponding to two-dimensional QCD (QCD{sub 2}) with adjoint fermions. We show that the bosonized model is equivalent to the fermion model only if a particular form of the WZNW action with a gauge-invariant integrand is chosen. For the exact correspondence, it is necessary to integrate over the ways the gauge group SU({ital N})/{ital Z}{sub {ital N}} is embedded into the full O({ital N}{sup 2}{minus}1) group for the bosonized matter field. For evenmore » {ital N}, one should also take into account the contributions of both disconnected components in O({ital N}{sup 2}{minus}1). In that case, {ital Z}{sub {ital I}}{proportional_to}{ital m}{sup {ital n}{sub 0}} for small fermion masses where 2{ital n}{sub 0} coincides with the number of fermion zero modes in a particular instanton background. The Taylor expansion of {ital Z}{sub {ital I}}/{ital m}{sup {ital n}{sub 0}} in mass involves only even powers of {ital m}, as it should. The physics of adjoint QCD{sub 2} is discussed. We argue that, for odd {ital N}, the discrete chiral symmetry {ital Z}{sub 2}{circle_times}{ital Z}{sub 2} present in the action is broken spontaneously down to {ital Z}{sub 2} and the fermion condensate {l_angle}{bar {lambda}}{lambda}{r_angle}{sub 0} is formed. The system undergoes a first order phase transition at {ital T}{sub {ital c}}=0 so that the condensate is zero at an arbitrary small temperature. It is not yet quite clear what happens for even {ital N}{ge}4. {copyright} {ital 1996 The American Physical Society.}« less
  • The {ital t}-{ital J} model in two dimensions is bosonized using a set of {ital N}, coupled two-dimensional Fermi-surface patches. Ignoring tunneling between the patches, the coherent tunneling of holes and the superfluid phase are suppressed. Within this scheme the system remains in the normal phase when temperature {ital T}{r_arrow}0. The main feature of this construction is the absence of screening of the dissipative transversal gauge field generated by the spinons. This dissipative gauge field is responsible for the non-Fermi-liquid behavior, which is manifested in the free energy and single-particle Green function. The deviation from Fermi-liquid behavior is due tomore » the {ital U}(1) gauge field, and at long distances a new exponent due to the holes is identified. Experimental consequences are discussed. {copyright} {ital 1996 The American Physical Society.}« less
  • A geometrical non-Abelian bosonization for the Fermi surface excitations is constructed. We introduce a unitary operator which generates the deformation of the Fermi surface which obeys non-Abelian Kac-Moody-Poisson brackets. We study the Hubbard model for {ital d}{ge}1, the charge part is a Fermi liquid at finite temperature and a Luttinger liquid for {ital d}=1 at {ital T}=0. The spin part is described by an 0(3) nonlinear sigma model. {copyright} {ital 1996 The American Physical Society.}