Spectral functions of non essentially selfadjoint operators

H. FALOMIR; P.A.G. PISANI

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL

IOP PUBLISHING LTD

Lugar: Londres; Año: 2012 vol. 45 p. 1 - 43

1751-8113

One of the many problems to which Dowker devoted his attention is the effectof a conical singularity in the base manifold on the behavior of the quantumfields. In particular, he studied the small-t asymptotic expansion of the heatkerneltrace on a cone and its effects on physical quantities as the Casimirenergy. In this paper, we review some peculiar results found in the last decade,regarding the appearance of non-standard powers of t, and even negative integerpowers of log t, in this asymptotic expansion for the self-adjoint extensions ofsome symmetric operators with singular coefficients. Similarly, we show thatthe ζ-function associated with these self-adjoint extensions presents an unusualanalytic structure.This article is part of a special issue of Journal of Physics A:Mathematical andTheoretical in honour of StuartDowker?s 75th birthday devoted to ?Applicationsof ζ-functions and other spectral functions in mathematics and physics?.PACS numbers: 02.30.Tb, 02.30.Sa, 03.65.Db