Kaluza-Klein pistons with noncommutative extra dimensions

Oikonomou, V. K.

doi:10.1007/s11232-011-0027-9

Cited by 2 publications

(1 citation statement)

References 36 publications

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“…Many aspects of the Casimir effect have been analyzed by studying fluctuations of the vacuum of a field theory compactified on a torus. This is, in particular, due to the association of the toroidal topology with the Dirichlet or Neumann boundary conditions [78,[139][140][141][142][143][144][145][146][147]. It is important to emphasize the nature of calculations in the local formulation, initiated by Brown and Maclay [148], to derive the energy-momentum tensor of quantum fields: a procedure that leads naturally to standard renormalization scheme associated with the Casimir effect.…”

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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Some developments of the Casimir effect in p-cavity of (D + 1)-dimensional space–time

Zhai

Lin

Feng

et al. 2014

Int. J. Mod. Phys. A

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The Casimir effect for rectangular boxes has been studied for several decades. But there are still some points unclear. Recently, there are new developments related to this topic, including the demonstration of the equivalence of the regularization methods and the clarification of the ambiguity in the regularization of the temperature-dependent free energy. Also, the interesting quantum spring was raised stemming from the topological Casimir effect of the helix boundary conditions. We review these developments together with the general derivation of the Casimir energy of the p-dimensional cavity in (D + 1)-dimensional spacetime, paying special attention to the sign of the Casimir force in a cavity with unequal edges. In addition, we also review the Casimir piston, which is a configuration related to rectangular cavity.

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Kaluza-Klein pistons with noncommutative extra dimensions

Cited by 2 publications

References 36 publications

Quantum field theory on toroidal topology: Algebraic structure and applications

Quantum field theory on toroidal topology: Algebraic structure and applications

Some developments of the Casimir effect in p-cavity of (D + 1)-dimensional space–time

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