Callias index formula revisited / Fritz Gesztesy and Marcus Waurick.
Material type:
TextSeries: Lecture notes in mathematics ; 2157.Publication details: Switzerland : Springer, 2016.Description: ix, 192 pages ; 24 cmISBN: - 9783319299761
- 514.74 23 G393
| Item type | Current library | Call number | Status | Date due | Barcode | Item holds | |
|---|---|---|---|---|---|---|---|
| Books | ISI Library, Kolkata | 514.74 G393 (Browse shelf(Opens below)) | Available | 137702 |
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| 514.74 F452 Global bifurcation of periodic solutions with symmetry | 514.74 F662 Algebraic aspects of integrable systems | 514.74 G247 Nonsmooth critical point theory and nonlinear boundary value problems | 514.74 G393 Callias index formula revisited / | 514.74 G559 Global and stochastic analysis with applications to mathematical physics | 514.74 G872 Global analysis : proceedings | 514.74 H355 First course in dynamics |
Includes bibliographical references and index.
1. Introduction --
2. Notational Conventions --
3. Functional Analytic --
4. On Schatten-von Neumann Classes and Trace Class --
5. Pointwise Estimates for Integral Kernels --
6. Dirac-Type --
7. Derivation of the Trace Formula :The Trace Class Result --
8. Derivation of the Trace Formula :Diagonal Estimates --
9. The Case n = 3 --
10. The Index Theorem and Some Consequences --
11. Perturbation Theory for the Helmholtz Equation --
12. The Proof of Theorem 10.2: The Smooth Case --
13. The Proof of Theorem 10.2: The General Case --
14. 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].
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.
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