The Limiting Absorption Principle for Massless Dirac Operators, Properties of Spectral Shift Functions, and an Application to the Witten Index of Non-Fredholm Operators

The author's primary motivation for writing this book was to express the Witten index of a certain class of non-Fredholm operators, generated from multi-dimensional, massless Dirac operators, in terms of appropriate underlying spectral shift functions. This goal required a detailed control over continuity properties (more precisely, the existence of Lebesgue points) for the spectral shift functions involved, and hence the bulk of this book is devoted to an exhaustive investigation of the spectral properties of multi-dimensional, massless Dirac operators.