Thermal behavior of the compactified 3-D gross-neveu model

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

doi:10.1590/s0103-97332006000700009

Cited by 4 publications

(3 citation statements)

References 7 publications

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“…Simple models describing such interaction are the Nambu-Jona-Lasinio model [93,94] and the Gross-Neveu model [95]. Both have been formulated on a torus, in order to study, as effective theories for quantum chromodynamics, the phase-transition in the confining/deconfining region [79,[96][97][98][99][100][101][102][103]. Beyond a phase diagram structure, this formalism provides a critical temperature for the confinement/deconfinement transition in accordance with lattice calculations.…”

Section: Introductionmentioning

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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Section: Introductionmentioning

confidence: 99%

Quantum field theory on toroidal topology: Algebraic structure and applications

Khanna

Malbouisson

et al. 2014

Physics Reports

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“…is the generalized Epstein zeta-function [30] defined for Re(ν) > 1/2. We then analytically continue Z b 2 1 (ν, a) to the whole complex ν-plane [31][32][33][34].…”

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confidence: 99%

Phase transition in the 3D massive Gross-Neveu model

Khanna

Malbouisson

et al. 2010

EPL

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We consider the 3-dimensional massive Gross-Neveu model at finite temperature as an effective theory for strong interactions. Using the Matsubara imaginary time formalism, we derive a closed form for the renormalized T -dependent four-point function. This gives a singularity, suggesting a phase transition. Considering the free energy we obtain the T -dependent mass, which goes to zero for some temperature. These results lead us to the conclusion that there is a second-order phase transition.Introduction. -The Gross-Neveu (GN) model [1], proposed as an effective model for quantum chromodynamics (QCD), has been analyzed extensively in recent years. In several cases, these studies consider the temperature effect, associated with fermion systems, in both particle and condensed matter physics [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. The motivations and the nature of such analysis are multiple, including investigations of the continuous and discrete chiral symmetry [6,7]. The version with N massless fermions in (2+1)dimensions, for instance, presents chirality-breaking in perturbative analysis, and its restoration at finite temperature [14]. This provides insight into the intricate structure of the hadronic matter, such as for the quark confinement/deconfinement transition [5,[15][16][17]. Due to such characteristics, the GN model is taken as a prototype for analysis of phase transitions in quantum field theory for fermions. In this sense, the search for analytical results is another aspect that attracts interest, in general [18], but in particular for N = 1, where lattice calculations are hard to carry out. In this note, we address the (2+1)-dimensional GN model at finite temperature, but with non-zero mass and one type of fermion.

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“…Over the last two decades or so, there has been a great deal of work analyzing the behavior of the Gross-Neveu (GN) model [1], originally proposed as an effective model for quantum chromodynamics [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,22]. Such model consists of a Dirac equation for massless particles with a self interacting non-linear term coming from a 4-fermion Lagrangian.…”

Section: Introductionmentioning

confidence: 99%