V V Nesterenko et al 2003 Class. Quantum Grav. 20 431 doi:10.1088/0264-9381/20/3/304
Non-smoothness of the boundary and the relevant heat kernel coefficients
V V Nesterenko1, I G Pirozhenko1 and J Dittrich2,3
Show affiliationsThe 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.
- PACS
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02.60.Lj Ordinary and partial differential equations; boundary value problems
- MSC
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58J32 Boundary value problems on manifolds
41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (See also 30E15)
- Subjects
- Dates
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Issue 3 (7 February 2003)
Received 13 July 2002
Published 15 January 2003
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Non-smoothness of the boundary and the relevant heat kernel coefficients
V V Nesterenko et al 2003 Class. Quantum Grav. 20 431
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