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

Thermo Field Dynamics and quantum algebras

E. Celeghini, S. De Martino, S. De Siena, Alfredo Iorio, M. Rasetti, Giuseppe Vitiello

Published Jan 1, 1998• 35 citations
OpenAlex

Abstract

The algebraic structure of Thermo Field Dynamics lies in the $q$-deformation of the algebra of creation and annihilation operators. Doubling of the degrees of freedom, tilde-conjugation rules, and Bogoliubov transformation for bosons and fermions are recognized as algebraic properties of $h_{q}(1)$ and of $h_{q}(1|1)$, respectively.

Related papers

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

Generalizations of the thermal Bogoliubov transformation

Elmfors, P., Hiroomi Umezawa

The thermal Bogoliubov transformation in thermo field dynamics is generalized in two respects. First, a generalization of the $\\alpha$--degree of freedom to tilde non--conserving representations is considered. Secondly, the usual $2\\times2$ Bogoliubov matrix is extended to a $4\\times4$ matrix including mixing of modes with non--trivial multiparticle correlations. The analysis is carried out for both bosons and fermions.

•Jan 1, 1993•11 citations

Unperturbed Representation in Non-Equilibrium Thermo Field Dynamics

Toshihico Arimitsu, Hiroomi Umezawa

A fundamental framework of thermo field dynamics (TFD), including non-equilibrium situations as well as equilibrium stuations, is formulated through a compact axiomatic form, in which no reference to reservoirs is needed, by considering quantum fields. The semi-free quantum fields in TFD are constructed in a way parallel to that of the usual quantum field theory without thermal degrees of freedom, i.e. in terms of orthonormalization relations among wave functions, the sum rule for wave functions, the divisor operator and the particle-antiparticle conjugation (C-conjugation).

Journal of the Physical Society of Japan•May 15, 1986•23 citations

Multi-mode q-oscillator algebras with q2(k + 1) = 1 and related thermo field dynamics

Ya-Jun Gao

A type of multi-mode q-oscillator algebra with q2(k + 1) = 1 is set up and the associated qk-thermo field dynamics is constructed for all k = 1,2,,∞ in a unified form. It is demonstrated that these qk-thermo field dynamics can all be nicely fitted into the algebraic formulation of statistical mechanics (axiomatized form for statistical physics). This means that we obtain infinitely many realizations of the algebraic scheme, which extend the consideration of Ojima [1981 Ann. Phys. 137 1] and contain the usual thermo field dynamics for the fermionic (k = 1) and bosonic (k = ∞) systems as special cases. As simple applications, the qk-statistical average of some operators are given.

Chinese Physics•May 14, 2002•1 citation

Multi—mode q—oscillator algebras with q^2（k＋1）=1 and related thermo field dynamics

高亚军

A type of multi-mode q-oscillator algebra with q^2(k+1)=1 is set up and the associated qk-thermo field dynamics is constructed for all k=1,2,…，∞ in a unified form.It is demonstrated that these qk-thermo field dynamics can all be nicely fitted into the algebraic formulation of statistical mechanics(axiomatized form for statistical physics).This means that we obtain infinitely many realizations of the algebraic scheme,which extend the consideration of Ojima [1981 Ann.Phys.137 1] and contain the usual thermo field dynamics for the fermionic (k=1) and bosonic (k=∞) systems as special cases.As simple applications,the qk-statistical average of some operators are given.

中国物理B：英文版•Jun 12, 2005•0 citations

Classical Fermionic Dynamics

Luther Rinehart

The formulation of classical mechanics applicable to fermionic degrees of freedom is presented in mathematically rigorous terms, including a description of how the mathematical structure relates to the quantization of the theory. Canonical transformations and the algebra of observables are defined and studied. A formula is given for the analog of the Poisson bracket. The quantization of the theory proceeds according to deformation quantization.

arXiv:1505.00237•May 1, 2015•0 citations
The algebraic structure of Thermo Field Dynamics lies in the qqq-deformation of the algebra of creation and annihilation operators. Doubling of the degrees of freedom, tilde-conjugation rules, and Bogoliubov transformation for bosons and fermions are recognized as algebraic properties of hq(1)h_{q}(1)hq​(1) and of hq(1∣1)h_{q}(1|1)hq​(1∣1), respectively.
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.
The thermal Bogoliubov transformation in thermo field dynamics is generalized in two respects. First, a generalization of the alpha\\alphaalpha--degree of freedom to tilde non--conserving representations is considered. Secondly, the usual 2times22\\times22times2 Bogoliubov matrix is extended to a 4times44\\times44times4 matrix including mixing of modes with non--trivial multiparticle correlations. The analysis is carried out for both bosons and fermions.
A fundamental framework of thermo field dynamics (TFD), including non-equilibrium situations as well as equilibrium stuations, is formulated through a compact axiomatic form, in which no reference to reservoirs is needed, by considering quantum fields. The semi-free quantum fields in TFD are constructed in a way parallel to that of the usual quantum field theory without thermal degrees of freedom, i.e. in terms of orthonormalization relations among wave functions, the sum rule for wave functions, the divisor operator and the particle-antiparticle conjugation (C-conjugation).
A type of multi-mode q-oscillator algebra with q2(k + 1) = 1 is set up and the associated qk-thermo field dynamics is constructed for all k = 1,2,,∞ in a unified form. It is demonstrated that these qk-thermo field dynamics can all be nicely fitted into the algebraic formulation of statistical mechanics (axiomatized form for statistical physics). This means that we obtain infinitely many realizations of the algebraic scheme, which extend the consideration of Ojima [1981 Ann. Phys. 137 1] and contain the usual thermo field dynamics for the fermionic (k = 1) and bosonic (k = ∞) systems as special cases. As simple applications, the qk-statistical average of some operators are given.
A type of multi-mode q-oscillator algebra with q^2(k+1)=1 is set up and the associated qk-thermo field dynamics is constructed for all k=1,2,…，∞ in a unified form.It is demonstrated that these qk-thermo field dynamics can all be nicely fitted into the algebraic formulation of statistical mechanics(axiomatized form for statistical physics).This means that we obtain infinitely many realizations of the algebraic scheme,which extend the consideration of Ojima [1981 Ann.Phys.137 1] and contain the usual thermo field dynamics for the fermionic (k=1) and bosonic (k=∞) systems as special cases.As simple applications,the qk-statistical average of some operators are given.