The Callias index formula revisited [electronic resource] / Fritz Gesztesy, Marcus Waurick.
Gesztesy, Fritz, 1953- author.; Waurick, Marcus, author.
2016
QA614.92
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Title The Callias index formula revisited [electronic resource] / Fritz Gesztesy, Marcus Waurick.
Author Gesztesy, Fritz, 1953- author.
ISBN 9783319299778 (electronic book)
3319299778 (electronic book)
9783319299761
331929976X
Published Switzerland : Springer, 2016.
Language English
Description 1 online resource (ix, 192 pages) : illustration.
Call Number QA614.92
Dewey Decimal Classification 514/.74
Summary 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 relativistic quantum mechanics, condensed matter physics, and quantum field theory), there is much interest in computing Fredholm indices of certain linear partial differential operators. In the late 1970's, Constantine Callias found a formula for the Fredholm index of a particular first-order differential operator (intimately connected to a supersymmetric Dirac-type operator) additively perturbed by a potential, shedding additional light on the Fedosov-Hörmander Index Theorem. As a byproduct of our proof we also offer a glimpse at special non-Fredholm situations employing a generalized Witten index.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Source of Description Online resource; title from PDF title page (SpringerLink, viewed July 8, 2016).
Added Author Waurick, Marcus, author.
Series Lecture notes in mathematics (Springer-Verlag) ; 2157.
Available in Other Form Print version: 9783319299761
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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.

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