Heat-kernel Coefficients and Spectra of the Vector Laplacians on Spherical Domains with Conical Singularities

The spherical domains \(S^d_\beta\) with conical singularities are a convenient arena for studying the properties of tensor Laplacians on arbitrary manifolds with such a kind of singular points. In this paper the vector Laplacian on \(S^d_\beta\) is considered and its spectrum is calculated exactly...

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Bibliographic Details
Published in:arXiv.org 1996-10
Main Authors: De Nardo, Lara, Fursaev, Dmitri V, Miele, Gennaro
Format: Article
Language:English
Subjects:
Coefficients
Domains
Mathematical analysis
Operators (mathematics)
Singularities
Tensors
Online Access:Get full text
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Summary:The spherical domains \(S^d_\beta\) with conical singularities are a convenient arena for studying the properties of tensor Laplacians on arbitrary manifolds with such a kind of singular points. In this paper the vector Laplacian on \(S^d_\beta\) is considered and its spectrum is calculated exactly for any dimension \(d\). This enables one to find the Schwinger-DeWitt coefficients of this operator by using the residues of the \(\zeta\)-function. In particular, the second coefficient, defining the conformal anomaly, is explicitly calculated on \(S^d_\beta\) and its generalization to arbitrary manifolds is found. As an application of this result, the standard renormalization of the one-loop effective action of gauge fields is demonstrated to be sufficient to remove the ultraviolet divergences up to the first order in the conical deficit angle.
ISSN:2331-8422
DOI:10.48550/arxiv.9610011