Skip to main content
SpringerLink
Log in
Book cover

The Callias Index Formula Revisited

  • Book
  • © 2016

Overview

Authors:
  1. Fritz Gesztesy

    1. Dept of Mathematics, University of Missouri, Columbia, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Marcus Waurick

    1. Institut für Analysis, TU Dresden, Dresden, Germany

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Offers a new, functional analytic approach to the Callias index theorem and generalises it considerably
  • Give a very detailed history and explain the background in great detail
  • Shows very clearly the connections with other areas throughout the manuscript
  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2157)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 49.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (14 chapters)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. Introduction

    • Fritz Gesztesy, Marcus Waurick
    Pages 1-8

  3. Notational Conventions

    • Fritz Gesztesy, Marcus Waurick
    Pages 9-11

  4. Functional Analytic Preliminaries

    • Fritz Gesztesy, Marcus Waurick
    Pages 13-21

  5. On Schatten–von Neumann Classes and Trace Class Estimates

    • Fritz Gesztesy, Marcus Waurick
    Pages 23-33

  6. Pointwise Estimates for Integral Kernels

    • Fritz Gesztesy, Marcus Waurick
    Pages 35-53

  7. Dirac-Type Operators

    • Fritz Gesztesy, Marcus Waurick
    Pages 55-63

  8. Derivation of the Trace Formula: The Trace Class Result

    • Fritz Gesztesy, Marcus Waurick
    Pages 65-76

  9. Derivation of the Trace Formula: Diagonal Estimates

    • Fritz Gesztesy, Marcus Waurick
    Pages 77-99

  10. The Case n = 3

    • Fritz Gesztesy, Marcus Waurick
    Pages 101-105

  11. The Index Theorem and Some Consequences

    • Fritz Gesztesy, Marcus Waurick
    Pages 107-117

  12. Perturbation Theory for the Helmholtz Equation

    • Fritz Gesztesy, Marcus Waurick
    Pages 119-129

  13. The Proof of Theorem 10.2: The Smooth Case

    • Fritz Gesztesy, Marcus Waurick
    Pages 131-150

  14. The Proof of Theorem 10.2: The General Case

    • Fritz Gesztesy, Marcus Waurick
    Pages 151-156

  15. A Particular Class of Non-Fredholm Operators L and Their Generalized Witten Index

    • Fritz Gesztesy, Marcus Waurick
    Pages 157-165

  16. Back Matter

    Pages 167-194
    Download chapter PDF
Back to top

Keywords

About this book

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.

Authors and Affiliations

  • Dept of Mathematics, University of Missouri, Columbia, USA

    Fritz Gesztesy

  • Institut für Analysis, TU Dresden, Dresden, Germany

    Marcus Waurick

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation