2002/07/31 by V. V. Nesterenko, I. G. Pirozhenko, J. Dittrich · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Boundary (topology) #Boundary value problem #Gas Dynamics and Kinetic Theory #Generalization #Gravitational singularity #Heat kernel #Kernel (algebra) #Laplace operator #Laplace transform #Mathematical analysis #Mathematics #Operator (biology) #Optics #Physics #Polygon (computer graphics) #Pure mathematics #Quantum Electrodynamics and Casimir Effect #Smoothness #Thermal Radiation and Cooling Technologies #Wedge (geometry) #hep-th
paper · pdf · doi:10.1088/0264-9381/20/3/304
published as Class.Quant.Grav. 20 (2003) 431-456 · 30 pages, LaTeX2e using iopart.cls, 1 figure in eps format, 3 tables; substantial changes are introduced in calculations concerning external sector
arxiv created 2002/12/03 · openalex publication_date 2003/01/15 · arxiv updated 2017/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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. An interesting result in the case of an external sector of a wedge is the contribution to the coefficient B1, that cannot be interpreted as a local one, i.e., it cannot be assigned to any singularity of the boundary. This finding is in contradiction with the generally accepted point of view that the heat kernel coefficients are determined by the local properties of the manifold boundary (in the case of a flat manifold). 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.