Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-07-04
Class.Quant.Grav. 20 (2003) 431-456
Physics
High Energy Physics
High Energy Physics - Theory
30 pages, LaTeX2e using iopart.cls, 1 figure in eps format, 3 tables; substantial changes are introduced in calculations conce
Scientific paper
The contributions to the heat kernel coefficients generated by the corners of the boundary are studied. For this purpose the internal and external sectors of a wedge and a cone are considered. These sectors are obtained by introducing, inside the wedge, a cylindrical boundary. Transition to a cone is accomplished by identification of the wedge sides. The basic result of the paper is the calculation of the individual contributions to the heat kernel coefficients generated by the boundary singularities. In the course of this analysis certain patterns, that are followed by these contributions, are revealed. The implications of the obtained results in calculations of the vacuum energy for regions with nonsmooth boundary are discussed. The rules for obtaining all the heat kernel coefficients for the minus Laplace operator defined on a polygon or in its cylindrical generalization are formulated.
Dittrich Jaroslav
Nesterenko V. V.
Pirozhenko Irina G.
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