Adiabatic decomposition of the zeta-determinant and the Dirichlet to Neumann operator

Jinsung Park; Krzysztof P. Wojciechowski

doi:10.1016/j.geomphys.2004.12.008

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Adiabatic decomposition of the zeta-determinant and the Dirichlet to Neumann operator

Jinsung Park·Krzysztof P. Wojciechowski

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Abstract

We prove an adiabatic decomposition formula of the zeta-determinant of the Laplace type operator with respect to Dirichlet boundary condition. We allow the non-invertible tangential operator. As a result, our adiabatic decomposition formula involves the scattering matrix over the manifold with cylindrical end. We also describe the adiabatic limit of the zeta-determinant of the Dirichlet to Neumann operator, which plays the essential role of Burghelea-Friedlander-Kappeler's Meyer-Vietoris type formula of the zeta determinant.

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Jinsung Park, Krzysztof P. Wojciechowski. 2005-12-21. Adiabatic decomposition of the zeta-determinant and the Dirichlet to Neumann operator. https://doi.org/10.1016/j.geomphys.2004.12.008

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