Topological Casimir effect in models with helical compact dimensions

Abstract

We investigate the influence of the helical compactification of spatial dimension on the local properties of the vacuum state for a charged scalar field with general curvature coupling parameter. A general background geometry is considered with rotational symmetry in the subspace with the coordinates appearing in the helical periodicity condition. It is shown that by a coordinate transformation the problem is reduced to the problem with standard quasiperiodicity condition in the same local geometry and with the effective compactification radius determined by the length of the compact dimension and the helicity parameter. As an application of the general procedure we have considered locally de Sitter spacetime with a helical compact dimension. By using the Hadamard function for the Bunch-Davies vacuum state, the vacuum expectation values of the field squared, current density, and energy-momentum tensor are studied. The topological contributions are explicitly separated and their asymptotics are described at early and late stages of cosmological expansion. An important difference, compared to the problem with quasiperiodic conditions, is the appearance of the nonzero off-diagonal component of the energy-momentum tensor and of the component of the current density along the uncompact dimension.

13 pages

References in corpus (30)

• Quantum Fields and Extended Objects in Space-Times with Constant Curvature Spatial Section
• Creation of a Compact Topologically Nontrivial Inflationary Universe
• Shape versus Volume: Making Large Flat Extra Dimensions Invisible
• Induced fermionic current in toroidally compactified spacetimes with applications to cylindrical and toroidal nanotubes
• Quantum field theory on toroidal topology: algebraic structure and applications
• Casimir effect in de Sitter spacetime with compactified dimension
• Topological Casimir effect in Maxwell Electrodynamics on a Compact Manifold
• Finite temperature fermionic condensate and currents in topologically nontrivial spaces
• Induced vacuum currents in anti-de Sitter space with toral dimensions
• Shadows of the Planck Scale: The Changing Face of Compactification Geometry
• Fermionic current from topology and boundaries with applications to higher-dimensional models and nanophysics
• Wightman function and vacuum densities in de Sitter spacetime with toroidally compactified dimensions
• Finite temperature current densities and Bose-Einstein condensation in topologically nontrivial spaces
• Scalar and fermionic vacuum currents in de Sitter spacetime with compact dimensions
• Hadamard function and the vacuum currents in braneworlds with compact dimensions: Two-branes geometry
• Vacuum currents in braneworlds on AdS bulk with compact dimensions
• The Casimir force of Quantum Spring in the (D+1)-dimensional spacetime
• Fermionic vacuum currents in topologically nontrivial braneworlds: Two-brane geometry
• Casimir effect for scalar current densities in topologically nontrivial spaces
• Fermionic currents in AdS spacetime with compact dimensions
• Fermionic currents in topologically nontrivial braneworlds
• Quantum Spring from the Casimir Effect
• Magnetic effects on spontaneous symmetry breaking/restoration in a toroidal topology
• Thermal Casimir effect for the scalar field in flat spacetime under a helix boundary condition
• Fermionic Casimir effect with helix boundary condition
• Loop correction to the scalar Casimir energy density and generation of topological mass due to a helix boundary condition in a scenario with Lorentz violation
• Casimir effect with a helix torus boundary condition
• The Shape of Compact Toroidal Dimensions $T_{\theta }^d$ and the Casimir Effect on $M^D\times T_{\theta }^d$ spacetime
• Casimir effect in toroidally compactified de Sitter spacetime
• Fermionic vacuum stresses in models with toroidal compact dimensions