On the Nonequilibrium Statistical Operator and Classical Thermofield Dynamics

Silva, Lourival M. da; Santana, A. E.; Vianna, J. D. M.

doi:10.1590/s0103-97331997000400025

Cited by 12 publications

(8 citation statements)

References 1 publication

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“…(189), with analytical extension given in Eq. (190). For s = 1 and D = 3, such that ν = s − (D − 2)/2 = 1/2, performing the subtraction of divergent terms, following the procedure of Section 6, and using K ±1/2 (z) = √ πe −z / √ 2z and ∞ n=1 e −ξn /n = − ln(1 − e −ξ ), the self-energy reads…”

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confidence: 99%

Quantum field theory on toroidal topology: Algebraic structure and applications

Khanna

Malbouisson

et al. 2014

Physics Reports

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The development of quantum theory on a torus has a long history, and can be traced back to the 1920s, with the attempts by Nordström, Kaluza and Klein to define a fourth spatial dimension with a finite size, being curved in the form of a torus, such that Einstein and Maxwell equations would be unified. Many developments were carried out considering cosmological problems in association with particles physics, leading to methods that are useful for areas of physics, in which size effects play an important role. This interest in finite size effect systems has been increasing rapidly over the last decades, due principally to experimental improvements. In this review, the foundations of compactified quantum field theory on a torus are presented in a unified way, in order to consider applications in particle and condensed matted physics. The theory on a torus Γ d D = (S 1 ) d × R D−d is developed from a Lie-group representation and c*-algebra formalisms. As a first application, the quantum field theory at finite temperature, in its real-and imaginary-time versions, is addressed by focussing on its topological structure, the torus Γ 1 4 . The toroidal quantum-field theory provides the basis for a consistent approach of spontaneous symmetry breaking driven by both temperature and spatial boundaries. Then the superconductivity in films, wires and grains are analyzed, leading to some results that are comparable with experiments. The Casimir effect is studied taking the electromagnetic and Dirac field on a torus. In this case, the method of analysis is based on a generalized Bogoliubov transformation, that separates the Green function into two parts: one is associated with the empty space-time, while the other describes the impact of compactification. This provides a natural procedure for calculating the renormalized energy-momentum tensor. Self interacting four-fermion systems, described by the Gross-Neveu and Nambu-Jona-Lasinio models, are considered. Then finite size effects on the hadronic phase structure are investigated, taking into account density and temperature. As a final application, effects of extra spatial dimensions are addressed, by developing a quantum electrodynamics in a five-dimensional space-time, where the fifth-dimension is compactified on a torus. The formalism, initially developed for particle physics, provides results compatible with other trials of probing the existence of extra-dimensions.

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confidence: 99%

Quantum field theory on toroidal topology: Algebraic structure and applications

Khanna

Malbouisson

et al. 2014

Physics Reports

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“…Este procedimento, que aparece em diversos textos didáticos, fica limitado pela impossibilidade de generalização para sistemas descritos por campos quânticos ou ainda em situações fora do equilíbrio. O procedimento variacional de Tisza é que foi utilizado nas teorias de campos, assim como foi, por exemplo, empregado por Zubarev para descrever processos fora do equilíbrio [35][36][37].…”

Section: O Princípio De Extremo De Tisza E Os Ensembles De Gibbs-einsunclassified

László Tisza, 110 anos: Origens da Física Térmica Moderna

Santana

Simon

2019

Rev. Bras. Ensino Fís.

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A axiomática de László Tisza da termodinâmica é revisitada, identificada a partir de cinco elementos constitutivos, e incluída em uma perspectiva histórica. Através de uma definição de medida, uma análise detalhada da associação do formalismo de Tisza com o experimento é conduzida. A ênfase da apresentação é para a relação da axiomatização de Tisza com os desenvolvimentos da física térmica no século XX, incluindo os trabalhos de Landau e colaboradores, e os desenvolvimentos que conduziram à teoria quântica de campos a temperatura finita. Palavras-chave: Termodinâmica, Física térmica, Temperatura, Axiomatização de Tisza.The László Tisza axiomatization of thermodynamics is revisited, considered from five constitutive elements, and included in a historical perspective. Using a definition of measurement, a detailed analysis of the Tisza approach, in association with experiments, is carried out. The emphasis in the presentation is on the relation of Tisza formulation with developments of the thermal physics in the 20th Century, including results derived by Landau and coworkers and the developments that led to the quantum field theory at finite temperature.

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“…Furthermore, the TFD vector space has been taken as a representation space for Lie algebras [15]. Thus, the equations of motion in TFD have been derived from a study of the Galilei and Poincaré symmetries [15,16]; Liouville-von Neumann equations have been introduced for the Klein-Gordan and Dirac field associated with the kinetic theory [17]; and a classical counterpart of TFD has been identified [18,19]. A constitutive element of this representation theory for Lie algebras is the doubling structure in the set of mappings defined in the TFD Hilbert space (actually, this doubling is present in any field formalism dealing with thermal phenomena [1]).…”

Section: Introductionmentioning

confidence: 99%

Thermofield Dynamics and Path-Integral Formalism

Siqueira

2007

Proceedings of Fifth International Conference on Mathematical Methods in Physics — PoS(IC2006)

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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.

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On the Nonequilibrium Statistical Operator and Classical Thermofield Dynamics

Cited by 12 publications

References 1 publication

Quantum field theory on toroidal topology: Algebraic structure and applications

Quantum field theory on toroidal topology: Algebraic structure and applications

László Tisza, 110 anos: Origens da Física Térmica Moderna

Thermofield Dynamics and Path-Integral Formalism

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