© 2017

Covariant Schrödinger Semigroups on Riemannian Manifolds

  • Develops basic vector-bundle-valued objects of geometric analysis from scratch

  • Gives a detailed proof of the Feynman-Kac fomula with singular potentials on manifolds

  • Includes previously unpublished results


Part of the Operator Theory: Advances and Applications book series (OT, volume 264)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Batu Güneysu
    Pages 1-19
  3. Batu Güneysu
    Pages 21-26
  4. Batu Güneysu
    Pages 85-100
  5. Batu Güneysu
    Pages 119-125
  6. Batu Güneysu
    Pages 167-195
  7. Back Matter
    Pages 197-239

About this book


This monograph discusses covariant Schrödinger operators and their heat semigroups on noncompact Riemannian manifolds and aims to fill a gap in the literature, given the fact that the existing literature on Schrödinger operators has mainly focused on scalar Schrödinger operators on Euclidean spaces so far. In particular, the book studies operators that act on sections of vector bundles. In addition, these operators are allowed to have unbounded potential terms, possibly with strong local singularities. 

The results presented here provide the first systematic study of such operators that is sufficiently general to simultaneously treat the natural operators from quantum mechanics, such as magnetic Schrödinger operators with singular electric potentials, and those from geometry, such as squares of Dirac operators that have smooth but endomorphism-valued and possibly unbounded potentials.

The book is largely self-contained, making it accessible for graduate and postgraduate students alike. Since it also includes unpublished findings and new proofs of recently published results, it will also be interesting for researchers from geometric analysis, stochastic analysis, spectral theory, and mathematical physics.


covariant Schrödinger semigroup heat semigroup Schrödinger operators Brownian motion on manifolds spectral theory

Authors and affiliations

  1. 1.Mathematisches InstitutHumboldt-Universität zu BerlinBerlinGermany

Bibliographic information