Small Mass Expansion of Functional Determinants on the Generalized Cone

Abstract

In this paper we compute the small mass expansion for the functional determinant of a scalar Laplacian defined on the bounded, generalized cone. In the framework of zeta function regularization, we obtain an expression for the functional determinant valid in any dimension for both Dirichlet and Robin boundary conditions in terms of the spectral zeta function of the base manifold. Moreover, as a particular case, we specify the base to be a $d$-dimensional sphere and present explicit results for $d=2,3,4,5$.

LaTeX, 23 pages

References in corpus (6)

• Iterated amplitudes in the high-energy limit
• Renormalized Effective Actions in Radially Symmetric Backgrounds I: Partial Wave Cutoff Method
• Functional determinants for general self-adjoint extensions of Laplace-type operators resulting from the generalized cone
• Renormalized Effective Actions in Radially Symmetric Backgrounds: Exact Calculations Versus Approximation Methods
• One-Loop Effective Action in Orbifold Compactifications
• Analytic Form of the QCD Instanton Determinant for Small Quark Mass

Cited by in corpus (6)

• Conical Casimir Pistons with Hybrid Boundary Conditions
• Heat Kernel Coefficients for Laplace Operators on the Spherical Suspension
• Zeta Determinant for Laplace Operators on Riemann Caps
• The Spectral Zeta Function for Laplace Operators on Warped Product Manifolds of the type $I{\times }_{f}N$
• Analytic Form of the QCD Instanton Determinant for Small Quark Mass
• Spectral functions of non essentially selfadjoint operators