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The Callias Index Formula Revisited

Record Type:	Language materials, printed : Monograph/item
Title/Author:	The Callias Index Formula Revisited/ by Fritz Gesztesy, Marcus Waurick.
Author:	Gesztesy, Fritz.
other author:	Waurick, Marcus.
Description:	IX, 192 p. 1 illus.online resource. :
Contained By:	Springer Nature eBook
Subject:	Partial differential equations. -
Online resource:	https://doi.org/10.1007/978-3-319-29977-8
ISBN:	9783319299778

The Callias Index Formula Revisited
Gesztesy, Fritz.

The Callias Index Formula Revisited[electronic resource] /by Fritz Gesztesy, Marcus Waurick. - 1st ed. 2016. - IX, 192 p. 1 illus.online resource. - Lecture Notes in Mathematics,21570075-8434 ;. - Lecture Notes in Mathematics,2144.

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.

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.

ISBN: 9783319299778

Standard No.: 10.1007/978-3-319-29977-8doiSubjects--Topical Terms:

1102982
Partial differential equations.

LC Class. No.: QA370-380

Dewey Class. No.: 515.353

The Callias Index Formula Revisited
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