Zeta Function Methods and Quantum Fluctuations

Abstract

A review of some recent advances in zeta function techniques is given, in problems of pure mathematical nature but also as applied to the computation of quantum vacuum fluctuations in different field theories, and specially with a view to cosmological applications.

17 pages, Talk given at the Conference ``Quantum Theory and Symmetries - 5'', Valladolid (Spain), July 22 - 28, 2007

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• Born Again Universe
• Finite Temperature Casimir Effect for Massless Majorana Fermions in a Magnetic Field
• Casimir Energy and Brane Stability
• Geometrically confined thermal field theory: Finite size corrections and phase transitions
• Casimir effect of a Lorentz-violating scalar in magnetic field
• Thermal effects on the Casimir energy of a Lorentz-violating scalar in magnetic field
• Slab Bag Fermionic Casimir effect, Chiral Boundaries and Vector Boson - Majorana Fermion Pistons
• Finite temperature Casimir effect for massive scalars in a magnetic field
• Casimir effect in Snyder Space
• Magnetic field corrections to the repulsive Casimir effect at finite temperature
• One-loop omega-potential of quantum fields with ellipsoid constant-energy surface dispersion law
• Report of the Detailed Calculation of the Effective Potential in Spacetimes with $S^1\times R^d$ Topology and at Finite Temperature
• Casimir effect with one large extra dimension
• Some Developments of the Casimir Effect in $p$-Cavity of $(D+1)$-Dimensional Spacetime
• Brane Stabilization and Regionality of Extra Dimensions
• Testing extra dimensions with boundaries using Newton's law modifications
• Thermal Casimir effect for a Dirac field on flat space with a nontrivial circular boundary condition
• Undecidability in Spacetime Geometry via the AdS/CFT Correspondence
• Equivalence of zeta function technique and Abel-Plana formula in regularizing the Casimir energy of hyper-rectangular cavities