Abstract
The goal of this paper is to compute the zeta function determinant for the massive Laplacian on Riemann caps (or spherical suspensions). These manifolds are defined as compact and boundaryless D-dimensional manifolds deformed by a singular Riemannian structure. The deformed spheres, considered previously in the literature, belong to this class. After presenting the geometry and discussing the spectrum of the Laplacian, we illustrate a method to compute its zeta regularized determinant. The special case of the deformed sphere is recovered as a limit of our general formulas.
| Original language | English |
|---|---|
| Article number | 023503 |
| Journal | Journal of Mathematical Physics |
| Volume | 52 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2011 Feb 3 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
Cite this
Zeta determinant for Laplace operators on Riemann caps. / Flachi, Antonino; Fucci, Guglielmo.
In: Journal of Mathematical Physics, Vol. 52, No. 2, 023503, 03.02.2011.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Zeta determinant for Laplace operators on Riemann caps
AU - Flachi, Antonino
AU - Fucci, Guglielmo
PY - 2011/2/3
Y1 - 2011/2/3
N2 - The goal of this paper is to compute the zeta function determinant for the massive Laplacian on Riemann caps (or spherical suspensions). These manifolds are defined as compact and boundaryless D-dimensional manifolds deformed by a singular Riemannian structure. The deformed spheres, considered previously in the literature, belong to this class. After presenting the geometry and discussing the spectrum of the Laplacian, we illustrate a method to compute its zeta regularized determinant. The special case of the deformed sphere is recovered as a limit of our general formulas.
AB - The goal of this paper is to compute the zeta function determinant for the massive Laplacian on Riemann caps (or spherical suspensions). These manifolds are defined as compact and boundaryless D-dimensional manifolds deformed by a singular Riemannian structure. The deformed spheres, considered previously in the literature, belong to this class. After presenting the geometry and discussing the spectrum of the Laplacian, we illustrate a method to compute its zeta regularized determinant. The special case of the deformed sphere is recovered as a limit of our general formulas.
UR - http://www.scopus.com/inward/record.url?scp=79952076369&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=79952076369&partnerID=8YFLogxK
U2 - 10.1063/1.3545705
DO - 10.1063/1.3545705
M3 - Article
AN - SCOPUS:79952076369
VL - 52
JO - Journal of Mathematical Physics
JF - Journal of Mathematical Physics
SN - 0022-2488
IS - 2
M1 - 023503
ER -