Mathematical Research Letters

Volume 9, Issue 1, January 2002 pp. 17-25.

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

Authors: Jinsung Park and Krzysztof P. Wojciechowski
Author institution: IUPUI (Indiana/Purdue)

Summary: 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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