Covariant Schrödinger Semigroups on Riemannian Manifolds - Batu Güneysu Gebunden

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 suff iciently 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 Since it also includes unpublished findings and new proofs of recently published results it will also be interesting for researchers from geometric analysis stochastic analysis spectral theory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..