Heat trace asymptotics with transmittal boundary conditions and quantum brane-world scenario

Abstract

We study the spectral geometry of an operator of Laplace type on a manifold with a singular surface. We calculate several first coefficients of the heat kernel expansion. These coefficients are responsible for divergences and conformal anomaly in quantum brane-world scenario.

latex, 25 pp

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• Wightman function and vacuum fluctuations in higher dimensional brane models
• Multiple reflection expansion and heat kernel coefficients
• Quantum fluctuations in brane-world inflation without inflaton on the brane
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• Integral Equations for Heat Kernel in Compound Media
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• Atiyah-Patodi-Singer Index Theorem for Domain Walls
• Functional determinants in higher dimensions using contour integrals
• Divergences in the vacuum energy for frequency-dependent interactions
• Asymptotics of the heat equation with `exotic' boundary conditions or with time dependent coefficients
• Interface Conformal Anomalies
• Path integral formulation of Hodge duality on the brane
• The ultrarelativistic limit of 2D dilaton gravity and its energy momentum tensor
• Vacuum polarization of a massive scalar field in a wormhole spacetime
• The Casimir effect for pistons with transmittal boundary conditions
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• Vacuum Energy of Quantum Fields in Classical Background Configurations