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Spectral functions of non essentially selfadjoint operators
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Paper
Spectral functions of non essentially selfadjoint operators
2012
Overview
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.
Publisher
Cornell University Library, arXiv.org
