LEADER 03876nam 22006255 450 001 996466769603316 005 20200701010953.0 010 $a3-319-29977-8 024 7 $a10.1007/978-3-319-29977-8 035 $a(CKB)3710000000734918 035 $a(DE-He213)978-3-319-29977-8 035 $a(MiAaPQ)EBC6305041 035 $a(MiAaPQ)EBC5591491 035 $a(Au-PeEL)EBL5591491 035 $a(OCoLC)952973283 035 $a(PPN)194285383 035 $a(EXLCZ)993710000000734918 100 $a20160628d2016 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe Callias Index Formula Revisited$b[electronic resource] /$fby Fritz Gesztesy, Marcus Waurick 205 $a1st ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016. 215 $a1 online resource (IX, 192 p. 1 illus.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2157 311 $a3-319-29976-X 320 $aIncludes bibliographical references and index. 327 $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. 330 $aThese lecture notes aim at providing a purely analytical and accessible proof of the Callias index formula. In various branches of mathematics (particularly, linear and nonlinear partial differential operators, singular integral operators, etc.) and theoretical physics (e.g., nonrelativistic and relativistic quantum mechanics, condensed matter physics, and quantum field theory), there is much interest in computing Fredholm indices of certain linear partial differential operators. In the late 1970?s, Constantine Callias found a formula for the Fredholm index of a particular first-order differential operator (intimately connected to a supersymmetric Dirac-type operator) additively perturbed by a potential, shedding additional light on the Fedosov-Hörmander Index Theorem. As a byproduct of our proof we also offer a glimpse at special non-Fredholm situations employing a generalized Witten index. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v2157 606 $aPartial differential equations 606 $aOperator theory 606 $aFunctional analysis 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aOperator Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12139 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 615 0$aPartial differential equations. 615 0$aOperator theory. 615 0$aFunctional analysis. 615 14$aPartial Differential Equations. 615 24$aOperator Theory. 615 24$aFunctional Analysis. 676 $a515.7 700 $aGesztesy$b Fritz$4aut$4http://id.loc.gov/vocabulary/relators/aut$066693 702 $aWaurick$b Marcus$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466769603316 996 $aThe Callias Index Formula Revisited$92004329 997 $aUNISA