SPECTRAL GEOMETRY AND ONE-LOOP DIVERGENCES ON MANIFOLDS WITH CONICAL SINGULARITIES

The geometrical form of the one-loop divergences induced by conical singularities of background manifolds is studied. To this aim the heat kernel asymptotic expansion on spaces having the structure C(alpha) x SIGMA near singular surface SIGMA is analysed. Surface corrections to standard second and third heat coefficients are obtained explicitly in terms of angle alpha of a cone C(alpha) and components of the Riemann tensor. These results are compared to ones to be already known for some particular cases. Physical aspects of the surface divergences are shortly discussed.