Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1995-05-10
Phys.Rept.266:1-126,1996
Physics
High Energy Physics
High Energy Physics - Theory
Latex file, 122 pages
Scientific paper
10.1016/0370-1573(95)00053-4
The heat-kernel expansion and $\zeta$-regularization techniques for quantum field theory and extended objects on curved space-times are reviewed. In particular, ultrastatic space-times with spatial section consisting in manifold with constant curvature are discussed in detail. Several mathematical results, relevant to physical applications are presented, including exact solutions of the heat-kernel equation, a simple exposition of hyperbolic geometry and an elementary derivation of the Selberg trace formula. With regards to the physical applications, the vacuum energy for scalar fields, the one-loop renormalization of a self-interacting scalar field theory on a hyperbolic space-time, with a discussion on the topological symmetry breaking, the finite temperature effects and the Bose-Einstein condensation, are considered. Some attempts to generalize the results to extended objects are also presented, including some remarks on path integral quantization, asymptotic properties of extended objects and a novel representation for the one-loop (super)string free energy.
Bytsenko Andrei
Cognola Guido
Vanzo Luciano
Zerbini Sergio
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