Quantum field theory on toroidal topology: algebraic structure and applications
arXiv:1409.1245 · doi:10.1016/j.physrep.2014.02.002
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
References in corpus (30)
- Interactions and phase transitions on graphene's honeycomb lattice
- AC conductivity of graphene: from tight-binding model to 2+1-dimensional quantum electrodynamics
- Theory of interacting electrons on the honeycomb lattice
- Chiral Gauge Theory for Graphene
- Quantum Hall effect and the topological number in graphene
- Phase structure of the massive chiral Gross-Neveu model from Hartree-Fock
- Emergence of Tricritical Point and Liquid-Gas Phase in the Massless 2+1 Dimensional Gross-Neveu Model
- Finite-size effects on the phase structure of the Nambu-Jona-Lasinio model
- Fermionic current densities induced by magnetic flux in a conical space with a circular boundary
- Fermionic condensate and Casimir densities in the presence of compact dimensions with applications to nanotubes
- Aspect-ratio dependence of thermodynamic Casimir forces
- Quantum fields in toroidal topology
- Precise calculation of transition frequencies of hydrogen and deuterium based on a least-squares analysis
- Dynamical Casimir Effect in two-atom cavity QED
- Fermionic condensate in a conical space with a circular boundary and magnetic flux
- The trigonometric Casimir connection of a simple Lie algebra
- Noncommutative Geometry and Symplectic Field Theory
- Spontaneous Symmetry Breaking as a Basis of Particle Mass
- Phase diagram of quark-antiquark and diquark condensates at finite temperature and density in the 3-dimensional Gross Neveu model
- First-order phase transitions in superconducting films: A Euclidean model
- Maximum Entanglement in Squeezed Boson and Fermion States
- Casimir Effect in closed spaces
- Phase transition in the 3-D massive Gross-Neveu model
- Casimir energies with finite-width mirrors
- Enhanced Symmetries of Orbifolds from Moduli Stabilization
- Magnetic and Electric Dipole Constraints on Extra Dimensions and Magnetic Fluxes
- Thermofield dynamics and twisted Poincaré symmetry on Moyal space-time
- Thermofield Dynamics for Twisted Poincare-Invariant Field Theories: Wick Theorem and S-matrix
- Gravitational Atom in Compactified Extra Dimensions
- Scalar Casimir effect between two concentric D-dimensional spheres