The Dirac operator has many useful applications in theoretical
physics and mathematics. This book provides a clear, concise and
self-contained introduction to the global theory of the Dirac
operator and to the analysis of spectral asymptotics with local or
nonlocal boundary conditions. The theory is introduced at a level
suitable for graduate students. Numerous examples are then given to
illustrate the peculiar properties of the Dirac operator, and the
role of boundary conditions in heat-kernel asymptotics and quantum
field theory. Topics covered include the introduction of
spin-structures in Riemannian and Lorentzian manifolds;
applications of index theory; heat-kernel asymptotics for operators
of Laplace type; quark boundary conditions; one-loop quantum
cosmology; conformally covariant operators; and the role of the
Dirac operator in some recent investigations of four-manifolds.
This volume provides graduate students with a rigorous introduction
and researchers with a invaluable reference to the Dirac operator
and its applications in theoretical physics.
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