Mathematical Research Letters

Volume 9 (2002)

Number 1

Scattering Theory and Adiabatic Decomposition of the $\z$-determinant of the Dirac Laplacian

Pages: 17 – 25

DOI: http://dx.doi.org/10.4310/MRL.2002.v9.n1.a2

Authors

Jinsung Park

Krzysztof P. Wojciechowski

Abstract

In this note we announce the adiabatic decomposition formula for the $\z$-determinant of the Dirac Laplacian. Theorem \ref{t:apssplit} of this paper extends the result of our earlier work (see \cite{JPKW1} and \cite{JPKW2}), which covered the case of the invertible tangential operator. The presence of the non-trivial kernel of the tangential operator requires careful analysis of the small eigenvalues of the Dirac Laplacian, which employs elements of scattering theory.

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