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

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

2003-01-16

arxiv.org/abs/math/0301170v3

Journal of Geometry and Physics, vol. 55 (2005) p. 241-266

Mathematics

Differential Geometry

final version

Scientific paper

10.1016/j.geomphys.2004.12.008

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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