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The Callias Index Formula Revisited

Fritz Gesztesy - Personal Name; Marcus Waurick - Personal Name;

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.

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Series Title: Lecture Notes in Mathematics
Call Number: -
Publisher: Cham : Springer., 2016
Collation: IX, 192
Language: English
ISBN/ISSN: 978-3-319-29977-8
Classification: NONE
Content Type: text
Media Type: computer
Carrier Type: -
Edition: -
Subject(s): Functional Analysis
Specific Detail Info: -
Statement of Responsibility: Fritz Gesztesy, Marcus Waurick

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Cataloger: Jemadi
Source: https://link.springer.com/content/pdf/10.1007/978-3-319-29977-8.pdf?pdf=button
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