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The Callias index formula revisited /

Gesztesy, Fritz, (1953-)

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The Callias index formula revisited /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	The Callias index formula revisited // Fritz Gesztesy, Marcus Waurick.
Author:	Gesztesy, Fritz,
other author:	Waurick, Marcus.
Published:	[Cham. Switzerland :Springer, : 2016.,
Description:	ix, 192 p. ;24 cm.
Subject:	Differential equations, Partial. -
ISBN:	9783319299761
ISSN:	0075-8434

The Callias index formula revisited /
Gesztesy, Fritz,1953-

The Callias index formula revisited /Fritz Gesztesy, Marcus Waurick. - [Cham. Switzerland :Springer,2016. - ix, 192 p. ;24 cm. - Lecture notes in mathematics,21570075-8434 ;. - Lecture notes in mathematics (Springer-Verlag) ;2157..

Includes bibliographical references (p. 185-189) and index.

Introduction --

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.

ISBN: 9783319299761EUR34.99

ISSN: 0075-8434

LCCN: 2016942549Subjects--Topical Terms:

518115
Differential equations, Partial.

LC Class. No.: QA614.92

Dewey Class. No.: 514.74

The Callias index formula revisited /
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008 170104s2016 sz b 001 0 eng d
010 $a 2016942549
020 $a 9783319299761 $q (pbk.) : $c EUR34.99
020 $a 331929976X $q (pbk.)
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020 $a 3319299778 $q (ebk.)
022 # $a 0075-8434
022 # $a 1617-9692(ebk.)
040 $a YDXCP $b eng
050 # 4 $a QA614.92
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090 $a QA3 $b .L28 v.2157
100 1 $a Gesztesy, Fritz, $d 1953- $3 726310
245 1 0 $a The Callias index formula revisited / $c Fritz Gesztesy, Marcus Waurick.
260 # $a [Cham. Switzerland : $b Springer, $c 2016.
300 $a ix, 192 p. ; $c 24 cm.
490 1 0 $a Lecture notes in mathematics, $x 0075-8434 ; $v 2157
504 $a Includes bibliographical references (p. 185-189) and index.
505 0 # $t Introduction -- $t Notational conventions -- $t Functional analytic -- $t On Schatten-von Neumann classes and trace class -- $t Pointwise estimates for integral kernels -- $t Dirac-type -- $t Derivation of the trace formula -- $t The trace class result -- $t Derivation of the trace formula -- $t Diagonal estimates -- $t The case n = 3 -- $t The index theorem and some consequences -- $t Perturbation theory for the Helmholtz equation -- $t The proof of theorem 10.2 : the smooth case -- $t The proof of theorem 10.2 : the general case -- $t A particular class of non-fredholm operators L and their generalized witten index -- $t Construction of the euclidean dirac algebra -- $t A counterexample to [22, Lemma 5].
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-Hörmander Index Theorem.As a byproduct of our proof we also offer a glimpse at special non-Fredholm situations employing a generalized Witten index.
650 # 0 $a Differential equations, Partial. $3 518115
650 # 0 $a Index theorems. $3 589026
700 1 # $a Waurick, Marcus. $3 2200310
830 0 $a Lecture notes in mathematics (Springer-Verlag) ; $v 2157. $3 3166093