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This book is based on lectures given at the first edition of the
Domoschool, the International Alpine School in Mathematics and
Physics, held in Domodossola, Italy, in July 2018. It is divided
into two parts. Part I consists of four sets of lecture notes.
These are extended versions of lectures given at the Domoschool,
written by well-known experts in mathematics and physics related to
General Relativity. Part II collects talks by selected
participants, focusing on research related to General Relativity.
This monograph discusses covariant Schroedinger 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 Schroedinger operators has mainly focused on scalar
Schroedinger 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
Schroedinger 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 Since it also includes unpublished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..
This book is based on lectures given at the first edition of the
Domoschool, the International Alpine School in Mathematics and
Physics, held in Domodossola, Italy, in July 2018. It is divided
into two parts. Part I consists of four sets of lecture notes.
These are extended versions of lectures given at the Domoschool,
written by well-known experts in mathematics and physics related to
General Relativity. Part II collects talks by selected
participants, focusing on research related to General Relativity.
This monograph discusses covariant Schroedinger 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 Schroedinger operators has mainly focused on scalar
Schroedinger 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
Schroedinger 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..
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