Quantum field theory on toroidal topology: algebraic structure and applications

Abstract

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.

89 pages, 16 figures

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Cited by in corpus (37)

• Finite-volume and magnetic effects on the phase structure of the three-flavor Nambu--Jona-Lasinio model
• Charged pion condensation in dense quark matter: Nambu--Jona-Lasinio model study
• Hadamard function and the vacuum currents in braneworlds with compact dimensions: Two-branes geometry
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• Finite-size effects on the Phase Structure of the Walecka Model
• Fermionic currents in AdS spacetime with compact dimensions
• Casimir effect for scalar current densities in topologically nontrivial spaces
• BCS-BEC crossover of atomic Fermi superfluid in a spherical bubble trap
• Fermionic currents in topologically nontrivial braneworlds
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• Lorentz Symmetry and IR Structure of The BFSS Matrix Model
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• Properties of size-dependent models having quasiperiodic boundary conditions
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• Spontaneous symmetry breaking in replica field theory
• Properties of neutral mesons in a hot and magnetized quark matter: size-dependent effects
• Dimensional reduction of a finite-size scalar field model at finite temperature
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• A Model to Study Finite-Size and Magnetic Effects on the Phase Transition of a Fermion Interacting System
• Critical behaviour of an effective relativistic mean field model in the presence of magnetic background and boundaries
• Inverse magnetic catalysis and size-dependent effects on the chiral symmetry restoration
• Casimir effect and Stefan-Boltzmann law in Yang-Mills theory at finite temperature
• Particle on a Torus Knot: Anholonomy and Hannay Angle
• Finite-size effects on the phase transition in a four- and six-fermion interaction model
• Some new results for the one-loop mass correction to the compactified $\lambda {\varphi }^4$ theory
• Finite-Size Effects in Disordered $\lambda {\varphi }^4$ Model
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• Feynman Amplitudes in Periodically Compactified Spaces -- Spin 0
• Finite size effects in the phase transition patterns of coupled scalar field systems
• Quantum forces in cavities
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