Decomposition of the Ζ - Determinant and Scattering Theory
نویسنده
چکیده
(1.3) M = M1 ∪M2 , M1 ∩M2 = Y = ∂M1 = ∂M2 . In this paper, we study the adiabatic decomposition of the ζ-determinant of D2, which describes the contributions in detζD coming from the submanifolds M1 and M2. Throughout the paper, we assume that the manifold M and the operator D have product structures in a neighborhood of the cutting hypersurface Y . Hence, there is a bicollar neighborhood N ∼= [−1, 1]u × Y of Y ∼= {0} × Y in M such that the Riemannian structure on M and the Hermitian structure on S are products of the corresponding structures over [−1, 1]u and Y when restricted to N , so that D has the following form,
منابع مشابه
Scattering Theory, the Adiabatic Decomposition of the Ζ-determinant and the Dirichlet to Neumann Operator
We also discuss the relation of our work to the earlier work on the decomposition of the ζ-determinant by Burghelea, Friedlander and Kappeler (from this point on referred to as BFK). The present work is companion to the paper [10] and in several places we refer to [10] for the proof of a given statement and a more detailed discussion. Let D : C(M ;S) → C(M ;S) be a compatible Dirac operator act...
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