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000756205 020__ $$a9783319299778$$q(electronic book)
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000756205 1001_ $$aGesztesy, Fritz,$$d1953-$$eauthor.
000756205 24514 $$aThe Callias index formula revisited$$h[electronic resource] /$$cFritz Gesztesy, Marcus Waurick.
000756205 264_1 $$aSwitzerland :$$bSpringer,$$c2016.
000756205 300__ $$a1 online resource (ix, 192 pages) :$$billustration.
000756205 336__ $$atext$$btxt$$2rdacontent
000756205 337__ $$acomputer$$bc$$2rdamedia
000756205 338__ $$aonline resource$$bcr$$2rdacarrier
000756205 4901_ $$aLecture notes in mathematics,$$x0075-8434 ;$$v2157
000756205 504__ $$aIncludes bibliographical references and index.
000756205 5050_ $$aIntroduction.-Notational Conventions -- Functional Analytic -- On Schatten-von Neumann Classes and Trace Class -- Pointwise Estimates for Integral Kernels -- Dirac-Type -- Derivation of the Trace Formula -- The Trace Class Result -- Derivation of the Trace Formula -- Diagonal Estimates -- The Case n = 3 -- The Index Theorem and Some Consequences -- Perturbation Theory for the Helmholtz Equation -- The Proof of Theorem 10.2: The Smooth Case -- The Proof of Theorem 10.2: The General Case -- A Particular Class of Non-Fredholm Operators L and Their Generalized Witten Index -- A: Construction of the Euclidean Dirac Algebra -- B: A Counterexample to [22, Lemma 5] -- References -- Index.
000756205 506__ $$aAccess limited to authorized users.
000756205 520__ $$aThese lecture notes aim at providing a purely analytical and accessible proof of the Callias index formula. In various branches of mathematics (particularly, linear and nonlinear partial differential operators, singular integral operators, etc.) and theoretical physics (e.g., nonrelativistic and relativistic quantum mechanics, condensed matter physics, and quantum field theory), there is much interest in computing Fredholm indices of certain linear partial differential operators. In the late 1970's, Constantine Callias found a formula for the Fredholm index of a particular first-order differential operator (intimately connected to a supersymmetric Dirac-type operator) additively perturbed by a potential, shedding additional light on the Fedosov-Hörmander Index Theorem. As a byproduct of our proof we also offer a glimpse at special non-Fredholm situations employing a generalized Witten index.
000756205 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed July 8, 2016).
000756205 650_0 $$aIndex theorems.
000756205 650_0 $$aDifferential equations, Partial.
000756205 7001_ $$aWaurick, Marcus,$$eauthor.
000756205 77608 $$iPrint version:$$z331929976X$$z9783319299761$$w(OCoLC)935185833
000756205 830_0 $$aLecture notes in mathematics (Springer-Verlag) ;$$v2157.
000756205 852__ $$bebk
000756205 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-319-29977-8$$zOnline Access$$91397441.1
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