Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1993-04-08
Commun.Math.Phys. 165 (1994) 233-260
Physics
High Energy Physics
High Energy Physics - Theory
40 pages
Scientific paper
10.1007/BF02099770
The functional determinant of an elliptic operator with positive, discrete spectrum may be defined as $e^{-Z'(0)}$, where $Z(s)$, the zeta function, is the sum $\sum_n^{\infty} \lambda_n^{-s}$ analytically continued to $s$ around the origin. In this paper $Z'(0)$ is calculated for the Laplace operator with Dirichlet boundary conditions inside polygons and simplices with the topology of a disc in the Euclidean plane. The domains we consider are hence piece--wise flat with corners on the boundary and in the interior. Our results are complementary to earlier investigations of the determinants on smooth surfaces with smooth boundaries. We have explicit closed integrated expressions for triangles and regular polygons.
Aurell Erik
Salomonson Per
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