The Callias Index Formula Revisited

• Main Authors: Gesztesy, Fritz (Author), Waurick, Marcus (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2016.
• Series: Lecture Notes in Mathematics, 2157
• Subjects: Mathematics.; Functional analysis.; Operator theory.; Partial differential equations.; Partial Differential Equations.; Operator Theory.; Functional Analysis.

These lecture notes aim at providing a purely analytical and accessible proof of the Callias index formula. In various branches of mathematics (particularly, linear and nonlinear partial differential operators, singular integral operators, etc.) and theoretical physics (e.g., nonrelativistic and rel...

Table of Contents:

• Introduction.-Notational Conventions
• Functional Analytic
• On Schatten–von Neumann Classes and Trace Class
• Pointwise Estimates for Integral Kernels
• Dirac-Type
• Derivation of the Trace Formula – The Trace Class Result
• Derivation of the Trace Formula – Diagonal Estimates
• The Case n = 3
• The Index Theorem and Some Consequences
• Perturbation Theory for the Helmholtz Equation
• The Proof of Theorem 10.2: The Smooth Case
• The Proof of Theorem 10.2: The General Case
• A Particular Class of Non-Fredholm Operators L and Their Generalized Witten Index
• A: Construction of the Euclidean Dirac Algebra
• B: A Counterexample to [22, Lemma 5]
• References
• Index.