Thermal Quantum Field Theory - Algebraic Aspects and Applications

Khanna, F. C.; Malbouisson, A. P. C.; Malbouisson, J. M. C.; Santana, A. E.

doi:10.1142/9789812818898

Cited by 121 publications

(255 citation statements)

References 0 publications

Supporting

Mentioning

229

Contrasting

Unclassified

Order By: Relevance

“…On the one hand, those states with real masses can propagate freely in the deconfined phase. On the other hand, the existence of complex poles of the propagator in the confined phase produces a strong damping avoiding the propagation of such states.Real time formalisms, as thermo-field dynamics or the Schwinger-Keldysh formalism, can be constructed through the analytic continuation of the Euclidean action [33][34][35][36][37][38][39]. Those formalisms double the number of degrees of freedom, providing the appearance of a 2 × 2 matrix propagator S ij .…”

mentioning

confidence: 99%

Thermal nonlocal Nambu–Jona-Lasinio model in the real time formalism

Loewe

Morales²,

Villavicencio³

2011

Phys. Rev. D

View full text Add to dashboard Cite

The real time formalism at finite temperature and chemical potential for the nonlocal NambuJona-Lasinio model is developed in the presence of a Gaussian covariant regulator. We construct the most general thermal propagator, by means of the spectral function. As a result, the model involves the propagation of massive quasiparticles. The appearance of complex poles is interpreted as a confinement signal, and, in this case, we have unstable quasiparticles with a finite decay width. An expression for the propagator along the critical line, where complex poles start to appear, is also obtained. A generalization to other covariant regulators is proposed. The Nambu-Jona-Lasinio model (NJL) has been vastly considered for studying nonperturbative aspects of QCD. Nowadays, it is mainly used to explore finite temperature and density effects in the frame of the mean-field approximation [1][2][3]. One of the big challenges in QCD is to understand the confinement mechanism and the dynamics behind confinement. Perturbative QCD cannot describe confinement and, although lattice QCD is able to reproduce successfully hadron properties, like masses and coupling constants [4], it has problems when dealing with finite baryon chemical potential (the sign problem). However, there are effective models which include explicitly confinement, as, for example, different versions of the bag model [5][6][7][8], Dyson-Schwinger models [9-13], or the Polyakov loop effective action coupled to DysonSchwinger or NJL models [14][15][16][17].The nonlocal NJL model (nNJL) is another attempt in this direction [18][19][20][21]. When the gluon degrees of freedom are integrated out in the QCD action, a nonlocal quark action emerges and confinement should be hidden there. The idea of the nNJL approach is to incorporate nonlocal vertices through the presence of appropriate regulators.Since the NJL model is nonrenormalizable, a momentum cutoff is needed in order to handle the UV divergences. The applicability of the model is, therefore, restricted to energy scales below the cutoff. Nonlocal extensions of the NJL model are designed to regularize the model in such a way that UV divergences are controlled, internal symmetries are preserved, and quark confinement is incorporated. The nNJL model has been extended to a finite temperature and density scenario [22][23][24][25][26][27][28][29][30][31][32] through the usual Matsubara formalism [33,34]. Here, nevertheless, the exact summation of Matsubara frequencies turns out to be cumbersome, due to the complicated shape of the regulators. In most cases, it is necessary to cut the series at some order.The idea of this work is to develop the finite temperature real time formalism for the nNJL model. In this way, we are able to calculate temperature corrections, providing a physical picture in terms of quasiparticles. On the one hand, those states with real masses can propagate freely in the deconfined phase. On the other hand, the existence of complex poles of the propagator in the confined phase produces a strong dam...

show abstract

mentioning

confidence: 99%

Thermal nonlocal Nambu–Jona-Lasinio model in the real time formalism

Loewe

Morales²,

Villavicencio³

2011

Phys. Rev. D

View full text Add to dashboard Cite

show abstract

“…The KMS conditions, carrying the anti-periodicity for fermions, imply that the Feynman rules are modified by the well-known Matsubara prescription [7],…”

Section: The Modelmentioning

confidence: 99%

“…Compactification of spatial dimensions [5,6] is considered in a similar way. An unified treatment, generalizing various approaches dealing with finite-temperature and spatialcompactification concurrently, has been constructed [7,8,9] These methods have been employed to investigate spontaneous symmetrybreaking induced by temperature and/or spatial constraints in some bosonic and fermionic models describing phase transitions in condensed-matter, statistical and particle physics; for instance, for describing the size-dependence of the transition temperature of superconducting films, wires and grains [10,11]; for investigating size-effects in first-and second-order transitions [12,13,14,15]; and for analyzing size and magnetic-field effects on the Gross-Neveu (GN) [16] and the Nambu-Jona-Lasinio (NJL) [17] models, taken as effective theories [18] for hadronic physics [19,20,21].…”

Section: Introductionmentioning

confidence: 99%

Finite-size effects on the phase transition in a four- and six-fermion interaction model

et al. 2014

View full text Add to dashboard Cite

“…Em geral, a estratégia utilizadaé tentar codificar uma dada estrutura matemática numa C * -Álgebra e a partir disso, obter informações sobre essa estrutura provando teoremas sobre a C * -Álgebra associadaà estrutura [10][11][12][13][14]. Na Física as C * -Álgebras desempenham um papel importante na formulação da Mecânica Estatística [15,16], na descrição algébrica na Teoria Quântica de Campos [17], em Geometrias não Comutativas [18] e em Teorias Térmicas [19][20][21][22][23], como a Dinâmica de Campos Térmicos [24].…”

Section: Introductionunclassified

C*-Álgebras e a Descrição da Mecânica Quântica

Floquet

Júnior

Trindade

et al. 2018

Rev. Bras. Ensino Fís.

View full text Add to dashboard Cite

Neste artigo apresentamos a Teoria das C * -Álgebras. Demonstramos dois importantes resultados que são: o Teorema de Gelfand, que associa toda C * -Álgebra Abelianaàs funções contínuas sobre um espaço Hausdorff compacto, e o Teorema de Gelfand-Neumark, que relaciona toda C * -Álgebra não Abeliana aos operadores lineares sobre um espaço de Hilbert. Em seguida, mapeamos a Mecânica Clássica dentro da teoria da C * -Álgebra, obtendo uma prescrição algébrica para os estados eàs observáveis clássicas. Ao estendermos essa construção para o caso Quântico, preservando a prescrição algébrica e utilizando o Princípio da Incerteza, obtemos que os estados quânticos devem ser descritos por vetores do Espaço de Hilbert enquanto que os observáveis quânticos são os operadores auto-adjuntos sobre este espaço; discutimos brevemente sobre aÁlgebra de Weyl. Palavras-chave: Mecânica Quântica, C * -Álgebras, Teorema de Gelfand-Neumark.In this paper we present the theory of C * -Algebras. We show two major results that are Gelfand's Theorem, which associates every Abelian C * -Algebra as continuous functions on a compact Hausdorff space, and the Gelfand-Neumark Theorem, which relates all non-Abelian C * -Algebra to linear operators on a Hilbert space. Then we map the Classical Mechanics into the C * -Algebra's theory, obtaining an algebraic prescription for classical states and observables. When we extend this construction to the Quantum case, preserving the algebraic prescriptions and using the Uncertainty Principle, we obtain that quantum states must be described by vectors in a Hilbert space while quantum observables are the self-adjoint operators on this space; we briefly discussed the Weyl's Algebra. Keywords: Quantum Mechanics, C * -Algebras, Gelfand-Neumark Theorem. IntroduçãoUma das inquietudes iniciais de quase todos os estudantes ao se depararem pela primeira vez com a Mecânica Quânticaé a sua descrição Matemática. Enquanto os estados na Mecânica Clássica são tipicamente vetores que guardam os dados de posição e momento de cada partícula do sistema (portanto, elementos de um espaço vetorial de dimensão finita), enquanto as observáveis são funções nesses espaços (como temperatura, pressão e energia, por exemplo), na Mecânica Quântica temos um modelo bem mais sofisticado. A necessidade de um Espaço de Hilbert para descrever os estados e de operadores auto-adjuntos para caracterizar os observáveis, quebra intuitivamente a noção clássica onde os estados e observáveis são elementos de um espaço de fase e funções contínuas sobre esse espaço, respectivamente. O presente artigo tem como objetivo mostrar que, se tomarmos a descrição da Mecânica Clássica baseada nas C * -Álgebras, podemos obter que a descrição Matemática * Endereço de correspondência: sergio.floquet@univasf.edu.br.para o caso Quânticoé naturalmente dada por operadores auto-adjuntos sobre um espaço de Hilbert, fazendo uso somente do Princípio da Incerteza. Essa abordagem se mostrou mais que profícua a partir da construção GNS (Gelfand-Neumark-Segal). Como muito da teori...

show abstract

Thermal Quantum Field Theory - Algebraic Aspects and Applications

Cited by 121 publications

References 0 publications

Thermal nonlocal Nambu–Jona-Lasinio model in the real time formalism

Thermal nonlocal Nambu–Jona-Lasinio model in the real time formalism

Finite-size effects on the phase transition in a four- and six-fermion interaction model

C*-Álgebras e a Descrição da Mecânica Quântica

Contact Info

Product

Resources

About