The Callias Index Formula Revisited

Nonfiction, Science & Nature, Mathematics, Functional Analysis, Differential Equations
Cover of the book The Callias Index Formula Revisited by Fritz Gesztesy, Marcus Waurick, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Fritz Gesztesy, Marcus Waurick ISBN: 9783319299778
Publisher: Springer International Publishing Publication: June 28, 2016
Imprint: Springer Language: English
Author: Fritz Gesztesy, Marcus Waurick
ISBN: 9783319299778
Publisher: Springer International Publishing
Publication: June 28, 2016
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer International Publishing

Cover of the book Euro-Par 2017: Parallel Processing by Fritz Gesztesy, Marcus Waurick
Cover of the book The Mathematics of Options by Fritz Gesztesy, Marcus Waurick
Cover of the book Computational Diffusion MRI by Fritz Gesztesy, Marcus Waurick
Cover of the book Guided Internet-Based Treatments in Psychiatry by Fritz Gesztesy, Marcus Waurick
Cover of the book Artificial Intelligence and Security by Fritz Gesztesy, Marcus Waurick
Cover of the book Targeting the IL-17 Pathway in Inflammatory Disorders by Fritz Gesztesy, Marcus Waurick
Cover of the book AETA 2017 - Recent Advances in Electrical Engineering and Related Sciences: Theory and Application by Fritz Gesztesy, Marcus Waurick
Cover of the book Advances in Computing by Fritz Gesztesy, Marcus Waurick
Cover of the book Flood Monitoring through Remote Sensing by Fritz Gesztesy, Marcus Waurick
Cover of the book The Nile River by Fritz Gesztesy, Marcus Waurick
Cover of the book Advanced Materials Processing and Manufacturing by Fritz Gesztesy, Marcus Waurick
Cover of the book Growing Stock Volume Estimation in Temperate Forested Areas Using a Fusion Approach with SAR Satellites Imagery by Fritz Gesztesy, Marcus Waurick
Cover of the book Controlling the Morphology of Polymers by Fritz Gesztesy, Marcus Waurick
Cover of the book Fluorescent Tools for Imaging Oxidative Stress in Biology by Fritz Gesztesy, Marcus Waurick
Cover of the book Mobility Patterns and Experiences of the Middle Classes in a Globalizing Age by Fritz Gesztesy, Marcus Waurick
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy