LEADER 03188cam a2200433 i 4500 001 991003531769707536 006 m o d 007 cr cn ---mpcbr 008 180807s2016 sz a ob 001 0 eng d 020 $a9783319299778 020 $a3319299778 024 7 $a10.1007/978-3-319-29977-8$2doi 035 $ab14348184-39ule_inst 040 $aBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematica$beng 082 04$a514.74$223 084 $aAMS 47-02 084 $aLC QA614.92 100 1 $aGesztesy, Fritz$066693 245 14$aThe Callias index formula revisited$h[e-book] /$cFritz Gesztesy, Marcus Waurick 264 1$aCham, Switzerland :$bSpringer,$c2016 300 $a1 online resource (ix, 192 pages) :$billustration 336 $atext$btxt$2rdacontent 337 $acomputer$bc$2rdamedia 338 $aonline resource$bcr$2rdacarrier 490 1 $aLecture notes in mathematics,$x0075-8434 ;$v2157 504 $aIncludes bibliographical references and index 505 0 $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 520 $aThese lecture notes aim at providing a purely analytical and accessible proof of the Callias index formula. In various branches of mathematics (particularly, linear and nonlinear partial differential operators, singular integral operators, etc.) and theoretical physics (e.g., nonrelativistic and relativistic quantum mechanics, condensed matter physics, and quantum field theory), there is much interest in computing Fredholm indices of certain linear partial differential operators. In the late 1970's, Constantine Callias found a formula for the Fredholm index of a particular first-order differential operator (intimately connected to a supersymmetric Dirac-type operator) additively perturbed by a potential, shedding additional light on the Fedosov-Hörmander Index Theorem. As a byproduct of our proof we also offer a glimpse at special non-Fredholm situations employing a generalized Witten index 650 0$aIndex theorems 650 0$aDifferential equations, Partial 700 1 $aWaurick, Marcus$eauthor$4http://id.loc.gov/vocabulary/relators/aut$0721074 773 0 $aSpringer eBooks 776 08$iPrinted edition:$z9783319299761 856 40$uhttps://link.springer.com/book/10.1007/978-3-319-29977-8$zAn electronic book accessible through the World Wide Web 907 $a.b14348184$b03-03-22$c07-08-18 912 $a991003531769707536 996 $aCallias index formula revisited$91412589 997 $aUNISALENTO 998 $ale013$b07-08-18$cm$d@ $e-$feng$gsz $h4$i0