Heat-kernel Coefficients and Spectra of the Vector Laplacians on Spherical Domains with Conical Singularities
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Bibliographic record
Abstract
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.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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