Quantum Fields and Extended Objects in Space-Times with Constant Curvature Spatial Section

摘要

The heat-kernel expansion and $\zeta$-regularization techniques for quantumfield theory and extended objects on curved space-times are reviewed. Inparticular, ultrastatic space-times with spatial section consisting in manifoldwith constant curvature are discussed in detail. Several mathematical results,relevant to physical applications are presented, including exact solutions ofthe heat-kernel equation, a simple exposition of hyperbolic geometry and anelementary derivation of the Selberg trace formula. With regards to thephysical applications, the vacuum energy for scalar fields, the one-looprenormalization of a self-interacting scalar field theory on a hyperbolicspace-time, with a discussion on the topological symmetry breaking, the finitetemperature effects and the Bose-Einstein condensation, are considered. Someattempts to generalize the results to extended objects are also presented,including some remarks on path integral quantization, asymptotic properties ofextended objects and a novel representation for the one-loop (super)string freeenergy.