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The Callias index formula revisited

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The Callias index formula revisited

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	The Callias index formula revisited/ by Fritz Gesztesy, Marcus Waurick.
作者:	Gesztesy, Fritz.
其他作者:	Waurick, Marcus.
出版者:	Cham :Springer International Publishing : : 2016.,
面頁冊數:	ix, 192 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
標題:	Index theorems. -
電子資源:	http://dx.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. - Cham :Springer International Publishing :2016. - ix, 192 p. :ill., digital ;24 cm. - Lecture notes in mathematics,21570075-8434 ;. - Lecture notes in mathematics ;1943..

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-Hormander 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:

1110683
Index theorems.

LC Class. No.: QA614.92

Dewey Class. No.: 514.74

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520 $a 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-Hormander 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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