Adiabatic decomposition of the zeta-determinant and Scattering theory

2001/11/05 by Jinsung Park, Park, Jinsung, Krzysztof P. Wojciechowski +1
Mathematics · #58J32 #58J52 #81Q70 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.DG #math.SP #msc:58J32 #msc:58J52 #msc:81Q70

paper · pdf · doi:10.48550/arxiv.math/0111046

final version

openalex publication_date 2001/11/05 · arxiv created 2005/12/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss the decomposition of the zeta-determinant of the square of the Dirac operator into contributions coming from the different parts of the manifold. The easy case was worked in the previous paper of authors. Due to the assumptions made on the operators in the previous paper, we were able to avoid the presence of the small eigenvalues which provide the large time contibution to the determinant. In the present work we analyze the general case. We offer a detailed analysis of the contribution made by the small eigenvalues.

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