Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1109.2278

Finite temperature Thirring model: from linearization through canonical transformations to correct normal form of thermofield solution

Semenov, V. V., S. É. Korenblit

Published Sep 11, 2011• 1 citation
arXivHTMLPDF

Abstract

It is shown that exact solvability of the finite temperature massless Thirring model, as well as of its zero temperature case, in canonical quantization scheme originates from the intrinsic hidden exact linearizability of Heisenberg equations by means of dynamical mapping onto the Schrödinger physical fields. The normal forms of different one- and two- parametric (thermo) field's solutions are obtained. They are connected with each other by making use of generalized conformal shift transformations. The sequential use of bosonic canonical transformations provides a correct renormalization, anticommutation and symmetry properties of these solutions. The dynamical role of inequivalent representations of 1+1-D free massless Dirac fields, that are induced by inequivalent representations of 1+1-D free massless (pseudo) scalar field, and the appearance of Schwinger terms are elucidated. The inequivalent vacuum is established as coherent state for SU(1,1) group. A new alternative sources of superselection rules are shown. A generalization of Ojima tilde conjugation rules is suggested, which reveals the properties of coherent state for SU(2) group for the fermionic thermal vacuum state and is useful for the thermofield bosonization. The notions of "hot" and "cold" thermofields are introduced to distinguish different thermofield representations giving the correct normal form of thermofield solution. The weak sense of definition of zero and finite temperature operator bosonization rules in the framework of thermofield dynamics is demonstrated.

DOI
10.48550/arxiv.1109.2278

Related papers

On fermionic tilde conjugation rules and thermal bosonization. Hot and cold thermofields

S. É. Korenblit, V. V. Semenov

A generalization of Ojima tilde conjugation rules is suggested, which is useful for the thermofield bosonization. The notion of hot and cold thermofields is introduced to distinguish different thermofield representations giving the correct normal form of thermofield solution for finite temperature Thirring model with correct renormalization and anticommutation properties.

arXiv:1108.5392•Physics of Particles and Nuclei Letters•Dec 1, 2011•1 citation

Fermion-Boson Equivalence in Thermo Field Dynamics

Yuji Nakawaki

To show the fermion-boson equivalence in thermo field dynamics, it is verified that thermal doublet of free massless fermion fields is equivalent to the corresponding doublet of Mandelstam expressions. Consequently operator solutions of Thirring and Schwinger models at finite temperature can be constructed by using zero-temperature ones.

Progress of Theoretical Physics•Dec 1, 1987•1 citation

QUANTUM GROUPS AND THERMO FIELD DYNAMICS

S. De Martino, Silvio De Siena, Giuseppe Vitiello

The algebraic structure of Thermo Field Dynamics for bosons can be fully incorporated in the q-deformation of the Weyl-Heisenberg algebra hq (1) . The doubling of the degrees of freedom, the set of the tilde-conjugation rules, the Bogoliubov transformation and its generator have a direct and simple interpretation in terms of operators and of properties of hq (1) . The notion of “thermal degree of freedom” introduced by Umezawa also finds a more specific formalization since the corresponding “thermal conjugate momentum” can be formally introduced, thus providing us with a set of canonical “thermal” variables.

International Journal of Modern Physics B•Jun 30, 1996•9 citations

Vacuum Diagrams in Perturbative Thermo Field Dynamics

H. Matsumoto, Hiroomi Umezawa, J. P. Whitehead

Perturbation theory in thermofield dynamics (a real time finite temperature quantum field theory) is formulated in the interaction representation and a diagrammatic expansion for the expectation value of time ordered products is derived solely on the basis of the thermal state condition and the algebraic properties of the operators. This new formulation has a much wider domain of applicability than those presented previously. The method is applicable even in the case of purely quantum mechanical systems. When certain bosonic operators, which commute with the unperturbed Hamiltonian, contribute to the renormalization of the thermal state vacuum the vacuum diagrams do not cancel in the usual way. It will be shown how these diagrams arise and how they may be computed.

Progress of Theoretical Physics•Jul 1, 1986•17 citations

Two-Dimensional Thermofield Bosonization

Amaral, R L P G, Belvedere, L V, Rothe, K D

The main objective of this paper is 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. In order 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.

•Apr 1, 2005•9 citations

Thermofield Dynamics and Path-Integral Formalism

Christyan Assis Siqueira

Thermofield Dynamics (TFD), a real time formalism for thermal quantum field theory, is formulated in terms of a path-integral approach following the Weinberg procedure.In order to assure precise rules for the development, we use a representation of Lie-algebras such that the TFD algebraic ingredients are derived, including the tilde conjugation rules.The association with the canonical formalism is obtained, and for the case of bosons, we introduce the Feynman diagrams and derive the n-point functions.

International Conference on Mathematical Methods in Physics (ICMP)•Apr 11, 2007•2 citations
It is shown that exact solvability of the finite temperature massless Thirring model, as well as of its zero temperature case, in canonical quantization scheme originates from the intrinsic hidden exact linearizability of Heisenberg equations by means of dynamical mapping onto the Schrödinger physical fields. The normal forms of different one- and two- parametric (thermo) field's solutions are obtained. They are connected with each other by making use of generalized conformal shift transformations. The sequential use of bosonic canonical transformations provides a correct renormalization, anticommutation and symmetry properties of these solutions. The dynamical role of inequivalent representations of 1+1-D free massless Dirac fields, that are induced by inequivalent representations of 1+1-D free massless (pseudo) scalar field, and the appearance of Schwinger terms are elucidated. The inequivalent vacuum is established as coherent state for SU(1,1) group. A new alternative sources of superselection rules are shown. A generalization of Ojima tilde conjugation rules is suggested, which reveals the properties of coherent state for SU(2) group for the fermionic thermal vacuum state and is useful for the thermofield bosonization. The notions of "hot" and "cold" thermofields are introduced to distinguish different thermofield representations giving the correct normal form of thermofield solution. The weak sense of definition of zero and finite temperature operator bosonization rules in the framework of thermofield dynamics is demonstrated.
The algebraic structure of Thermo Field Dynamics for bosons can be fully incorporated in the q-deformation of the Weyl-Heisenberg algebra hq (1) . The doubling of the degrees of freedom, the set of the tilde-conjugation rules, the Bogoliubov transformation and its generator have a direct and simple interpretation in terms of operators and of properties of hq (1) . The notion of “thermal degree of freedom” introduced by Umezawa also finds a more specific formalization since the corresponding “thermal conjugate momentum” can be formally introduced, thus providing us with a set of canonical “thermal” variables.
Perturbation theory in thermofield dynamics (a real time finite temperature quantum field theory) is formulated in the interaction representation and a diagrammatic expansion for the expectation value of time ordered products is derived solely on the basis of the thermal state condition and the algebraic properties of the operators. This new formulation has a much wider domain of applicability than those presented previously. The method is applicable even in the case of purely quantum mechanical systems. When certain bosonic operators, which commute with the unperturbed Hamiltonian, contribute to the renormalization of the thermal state vacuum the vacuum diagrams do not cancel in the usual way. It will be shown how these diagrams arise and how they may be computed.
The main objective of this paper is 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. In order 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.
Thermofield Dynamics (TFD), a real time formalism for thermal quantum field theory, is formulated in terms of a path-integral approach following the Weinberg procedure.In order to assure precise rules for the development, we use a representation of Lie-algebras such that the TFD algebraic ingredients are derived, including the tilde conjugation rules.The association with the canonical formalism is obtained, and for the case of bosons, we introduce the Feynman diagrams and derive the n-point functions.