TY  - BOOK
AU  - Gesztesy,Fritz
AU  - Waurick,Marcus
ED  - SpringerLink (Online service)
TI  - The Callias Index Formula Revisited
T2  - Lecture Notes in Mathematics,
SN  - 9783319299778
AV  - QA370-380 
U1  - 515.353 23
PY  - 2016///
CY  - Cham
PB  - Springer International Publishing, Imprint: Springer
KW  - Differential equations, partial
KW  - Operator theory
KW  - Functional analysis
KW  - Partial Differential Equations
KW  - Operator Theory
KW  - Functional Analysis
N1  - Introduction.-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
N2  - 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
UR  - https://doi.org/10.1007/978-3-319-29977-8
ER  -