Spectral functions of non essentially selfadjoint operators

Abstract

One of the many problems to which J.S. Dowker devoted his attention is the effect of a conical singularity in the base manifold on the behavior of the quantum fields. In particular, he studied the small-$t$ asymptotic expansion of the heat-kernel trace on a cone and its effects on physical quantities, as the Casimir energy. In this article we review some peculiar results found in the last decade, regarding the appearance of non-standard powers of $t$, and even negative integer powers of $\log t$, in this asymptotic expansion for the selfadjoint extensions of some symmetric operators with singular coefficients. Similarly, we show that the $\zeta$-function associated to these selfadjoint extensions presents an unusual analytic structure.

57 pages, 1 figure. References added. Version to appear in the special volume of Journal of Physics A in honor of Stuart Dowker's 75th birthday. PACS numbers: 02.30.Tb, 02.30.Sa, 03.65.Db

References in corpus (1)

• Small Mass Expansion of Functional Determinants on the Generalized Cone

Cited by in corpus (1)

• A New Example of the Effects of a Singular Background on the Zeta Function