Zeta function determinant of the Laplace operator on the $D$-dimensional ball
M. Bordag, B. Geyer, K. Kirsten (Institute for Theoretical Physics,, Leipzig University, Germany), E. Elizalde (CEAB, CSIC, Cam\'i de Santa, B\`arbara, Departament d'ECM, IFAE, Facultat de F{\ii}sica, Universitat, de Barcelona, Spain)
TL;DR
This paper introduces a direct method for calculating the zeta function determinant of the Laplace operator on D-dimensional balls, providing explicit formulas for various boundary conditions and dimensions.
Contribution
It offers a novel direct approach to compute functional determinants of the Laplace operator on balls for any dimension, including explicit results for specific cases.
Findings
Formulas derived for dimensions D=2 to 6
Applicable to Dirichlet and Robin boundary conditions
Simplifies calculation of determinants for arbitrary D
Abstract
We present a direct approach for the calculation of functional determinants of the Laplace operator on balls. Dirichlet and Robin boundary conditions are considered. Using this approach, formulas for any value of the dimension, , of the ball, can be obtained quite easily. Explicit results are presented here for dimensions and .
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