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also includes unpublished findings and new proofs of recently published results it will also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..
