An Extension of the Chowla-Selberg Formula Useful in Quantizing with the Wheeler-De Witt Equation

Abstract

The two-dimensional inhomogeneous zeta-function series (with homogeneous part of the most general Epstein type): \[ \sum_{m,n \in \mbox{\bf Z}} (am^2+bmn+cn^2+q)^{-s}, \] is analytically continued in the variable $s$ by using zeta-function techniques. A simple formula is obtained, which extends the Chowla-Selberg formula to inhomogeneous Epstein zeta-functions. The new expression is then applied to solve the problem of computing the determinant of the basic differential operator that appears in an attempt at quantizing gravity by using the Wheeler-De Witt equation in 2+1 dimensional spacetime with the torus topology.

14 pages (small typo errors corrected and 2page improvement of physical applications), LaTeX file, UB-ECM-PF 94/7

References in corpus (2)

• Zeta Functions and the Casimir Energy
• Notes on the (2+1)-Dimensional Wheeler-DeWitt Equation

Cited by in corpus (13)

• Finite temperature Casimir energy in closed rectangular cavities: a rigorous derivation based on zeta function technique
• Explicit Zeta Functions for Bosonic and Fermionic Fields on a Noncommutative Toroidal Spacetime
• Matching the observational value of the cosmological constant
• Casimir energy of a massive field in a genus-1 surface
• Finite temperature Casimir effect for massive scalar field in spacetime with extra dimensions
• On the issue of imposing boundary conditions on quantum fields
• Dynamical approach to the Casimir effect
• Finite Temperature Casimir Effect for a Massless Fractional Klein-Gordon field with Fractional Neumann Conditions
• Three dimensional Casimir piston for massive scalar fields
• Zeta function regularization in Casimir effect calculations and J.S. Dowker's contribution
• Casimir effect with a helix torus boundary condition
• Topological symmetry breaking of self--interacting fractional Klein--Gordon field on toroidal spacetime
• Stochastic Quantization and Casimir Forces