Properties of size-dependent models having quasiperiodic boundary conditions

Cavalcanti, E.; Linhares, C. A.; Malbouisson, A. P. C.

doi:10.1142/s0217751x18500082

Cited by 9 publications

(7 citation statements)

References 70 publications

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“…The remaining infinite sum can be identified as an Epstein-Hurwitz zeta function [18] and leads -after an analytic continuation -to the sum over modified Bessel functions of the second kind K ν (x); see Refs. [5,19] for further details. The function I D,d ρ (M 2 ; L α ) reads in the case of d = 2…”

Section: The Modelmentioning

confidence: 99%

Dimensional reduction of a finite-size scalar field model at finite temperature

et al. 2019

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We investigate the process of dimensional reduction of one spatial dimension in a thermal scalar field model defined in D dimensions (inverse temperature and D − 1 spatial dimensions). We obtain that a thermal model in D dimensions with one of the spatial dimensions having a finite size L is related to the finite temperature model with just D − 1 spatial dimensions and no finite size. Our results are obtained for one-loop calculations and for any dimension D. For example, in D = 4 we have a relationship between a thin film with thickness L at finite temperature and a surface at finite temperature. We show that, although a strict dimensional reduction is not allowed, it is possible to define a valid prescription for this procedure. * erich@cbpf.br †

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Section: The Modelmentioning

confidence: 99%

Dimensional reduction of a finite-size scalar field model at finite temperature

et al. 2019

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“…One scenario where this could be justified is when considering a complex scalar field coupled to a constant gauge field along the restricted spatial direction, as discussed in Ref. [35] and references therein.…”

Section: A Energy-momentum Tensor For Scalar Fieldsmentioning

confidence: 99%

Quantum forces in cavities

Cavalcanti

Malbouisson

2022

Phys. Rev. D

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We present an alternative route to investigate quantum forces in a cavity, for both a free scalar field and a free fermionic field. Considering a generalized Matsubara procedure, we compute the quantum pressure on the boundaries of a compactified space in a thermal bath. Also, considering both periodic and antiperiodic boundary conditions in the cavity, we discuss the attractive or repulsive character of the quantum forces. Our results highlight the relevance and interdisciplinarity of the generalized Matsubara procedure as a theoretical platform to manage quantum phenomena in nontrivial topologies.

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“…However, there is freedom regarding the boundary condition imposed on the spatial direction. In the context of quantum field theories at toroidal topologies it has been discussed the use of periodic and antiperiodic boundary conditions [30,31], its extension to quasiperiodic boundary conditions [33] and also the use of Dirichlet and Neumann boundary conditions [37]. We consider a scenario with d = 2 compactifications, after computing the remaining D − 2 integrals using dimensional regularization we obtain that the one-loop Feynman amplitude for each boundary condition (b.c.)…”

Section: Generic Model and Boundary Conditionsmentioning

confidence: 99%

“…Recently, in the context of phase transitions, it has been obtained that the minimal size of the system depends on the boundary conditions imposed on the spatial restriction. This analysis was done both for bosonic and fermionic models and a quasiperiodic boundary condition was applied which interpolates between the periodic and antiperiodic boundary conditions [33].…”

Section: Introductionmentioning

confidence: 99%

Effect of boundary conditions on dimensionally reduced field-theoretical models at finite temperature

Cavalcanti

Linhares²,

Lourenço

et al. 2019

Phys. Rev. D

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Here we understand dimensional reduction as a procedure to obtain an effective model in D − 1 dimensions that is related to the original model in D dimensions. To explore this concept we use both a self-interacting fermionic model and self-interacting bosonic model. Furthermore, in both cases, we consider different boundary conditions in space: periodic, antiperiodic, Dirichlet and Neumann. For bosonic fields, we get the so defined dimensional reduction. Taking the simple example of a quartic interaction, we obtain that the boundary condition (periodic, Dirichlet, Neumann) influence the new coupling of the reduced model. For fermionic fields, we get the curious result that the model obtained reducing from D dimensions to D − 1 dimensions is distinguishable from taking into account a fermionic field originally in D − 1 dimensions. Moreover, when one considers antiperiodic boundary condition in space (both for bosons or fermions) it is found that the dimensional reduction is not allowed. * erich@cbpf.br †

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Properties of size-dependent models having quasiperiodic boundary conditions

Cited by 9 publications

References 70 publications

Dimensional reduction of a finite-size scalar field model at finite temperature

Dimensional reduction of a finite-size scalar field model at finite temperature

Quantum forces in cavities

Effect of boundary conditions on dimensionally reduced field-theoretical models at finite temperature

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