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The Callias Index Formula Revisited: 2157 (Lecture Notes in Mathematics, 2157) - Softcover

Gesztesy, Fritz; Waurick, Marcus

 
9783319299761: The Callias Index Formula Revisited: 2157 (Lecture Notes in Mathematics, 2157)
Softcover
ISBN 10: 331929976X ISBN 13: 9783319299761
Publisher: Springer, 2016

Synopsis

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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From the Back Cover

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.

"About this title" may belong to another edition of this title.

Publisher
Springer
Publication date
2016
Language
English
ISBN 10 
331929976X
ISBN 13 
9783319299761
Binding
Paperback
Edition number
1
Number of pages
201