Lecture Notes in Mathematics

The Callias Index Formula Revisited

Authors: Gesztesy, Fritz, Waurick, Marcus

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  • Offers a new, functional analytic approach to the Callias index theorem and generalises it considerably
  • Give a very detailed history and explain the background in great detail
  • Shows very clearly the connections with other areas throughout the manuscript
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  • ISBN 978-3-319-29977-8
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Softcover $49.99
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  • ISBN 978-3-319-29976-1
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About this book

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.

Table of contents (14 chapters)

Table of contents (14 chapters)

Buy this book

eBook $39.99
price for USA in USD (gross)
  • ISBN 978-3-319-29977-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.99
price for USA in USD
  • ISBN 978-3-319-29976-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Callias Index Formula Revisited
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2157
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-29977-8
DOI
10.1007/978-3-319-29977-8
Softcover ISBN
978-3-319-29976-1
Series ISSN
0075-8434
Edition Number
1
Number of Pages
IX, 192
Number of Illustrations
1 b/w illustrations
Topics