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

Cavalcanti, E.; Lourenço, José André; Linhares, C. A.; Malbouisson, A. P. C.

doi:10.1103/physrevd.99.025007

Cited by 10 publications

(13 citation statements)

References 22 publications

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“…To explore this we need to evaluate I D,2 ρ at a very small length L. We proceed as in Ref. [34] and use a integral representation of K ν in the complex plane,…”

Section: Dimensional Reductionmentioning

confidence: 99%

“…This first case was the object of study in a previous article where we explored the subject in further detail [34]. We take the case of periodic boundary conditions, Eq.…”

Section: A Bosonic Field : Periodic Boundary Conditions In Spacementioning

confidence: 99%

“…We have previously found [34] that for bosonic fields at the 1-loop level the so-called dimensional reduction is obtained when one considers periodic boundary condition in space. In this article, we extend this analysis so that we consider a few more boundary conditions: Dirichlet, Neumann and antiperiodic.…”

Section: Introductionmentioning

confidence: 99%

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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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“…To explore this we need to evaluate I D,2 ρ at a very small length L. We proceed as in Ref. [34] and use a integral representation of K ν in the complex plane,…”

Section: Dimensional Reductionmentioning

confidence: 99%

“…This first case was the object of study in a previous article where we explored the subject in further detail [34]. We take the case of periodic boundary conditions, Eq.…”

Section: A Bosonic Field : Periodic Boundary Conditions In Spacementioning

confidence: 99%

See 1 more Smart Citation

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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“…Around 2010, a further approach in form of the CFRD Bell inequalities was obtained [23], [24], [25]. From the basic LHVT expression (4) for mean values a Bell inequality for bipartite systems with two observables per sub-system is given by…”

Section: Cfrd (2007-2011) Bell Inequalitiesmentioning

confidence: 99%

Bell non-locality in macroscopic systems

Dalton

2019

Eur. Phys. J. Spec. Top.

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The categorization of quantum states for composite systems as either separable or entangled, or alternatively as Bell local or Bell non-local states based on local hidden variable theory is reviewed in Sections 1 and 2, focusing on simple bipartite systems. The significance of states demonstrating Bell non-locality for settling the long standing controversy between the Copenhagen interpretation of the quantum measurement process involving "collapse of the wave-function" and the alternative interpretation based on pre-existing hidden variables is emphasized. Although experiments demonstrating violations of Bell locality in microscopic systems have now been carried out (see Section 3), there is current interest in finding Bell non-locality in quantum systems on a macroscopic scale, since this is a regime where a classical hidden variable theory might still apply. Progress towards finding macroscopic quantum states that violate Bell inequalities is reviewed in Section 4.A new test for Bell non-locality that applies when the sub-system measured quantities are spin components with large outcomes is described, and applied to four mode systems of identical massive bosons in Bose-Einstein condensates.

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“…IV), so we are close to the bulk scenario without compactifications. Both paths are equivalent and one could transport from one to another [75,76], but each one of them is more useful in one regime (near the dimensional reduction or the bulk), due to quicker convergence. After this, we illustrate the representation by showing some diagrams in Sec.…”

Section: Introductionmentioning

confidence: 99%

Feynman Amplitudes in Periodically Compactified Spaces -- Spin 0

Cavalcanti

2021

Preprint

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We propose an extension of the Schwinger parametric representation for Feynman amplitudes in D euclidean dimensions to a scenario where d dimensions are compactified (d < D) through the introduction of periodic boundary conditions in space. We obtain two valid representations, one useful near the bulk (large compactification length) and another useful near the dimensional reduction (small compactification length). Also, to illustrate, we exhibit some Feynman amplitudes up to three loops in a compactified scalar field theory.

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

Cited by 10 publications

References 22 publications

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

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

Bell non-locality in macroscopic systems

Feynman Amplitudes in Periodically Compactified Spaces -- Spin 0

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