The heat kernel expansion is a very convenient tool for studying one-loop divergences,
anomalies and various asymptotics of the effective action. The aim of this report is to collect …

We provide a review of both new experimental and theoretical developments in the Casimir
effect. The Casimir effect results from the alteration by the boundaries of the zero-point …

The study of general two-dimensional models of gravity allows to tackle basic questions of
quantum gravity, bypassing important technical complications which make the treatment in …

The literature on the spectral analysis of second order elliptic differential operators contains
a great deal of information on the spectral functions for explicitly known spectra. The same is …

We compare the one-loop corrections to the entropy of a black hole, from quantum fields of
spin zero, one-half, and one, to the entropy of entanglement of the fields. For fields of spin …

A great deal of progress has been made recently in the field of asymptotic formulas that arise
in the theory of Dirac and Laplace type operators. Asymptotic Formulae in Spectral …

We present a very quick and powerful method for the calculation of heat kernel coefficients. It
makes use of rather common ideas, as integral representations of the spectral sum, Mellin …

We show that in brane-world scenarios with warped extra dimensions, the Casimir force due
to bulk matter fields may be sufficient to stabilize the radion field φ. In particular, we calculate …

This book reflects our own struggle to understand the semiclassical behaviour of quantized
fields in the presence of boundaries. Along many years, motivated by the problems of …

We present a direct approach for the calculation of functional determinants of the Laplace
operator on balls. Dirichlet and Robin boundary conditions are considered. Using this …