Dirac Operators and Spectral Geometry
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Dirac Operators and Spectral Geometry by Giampiero Esposito
Book DescriptionThe 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 non-local 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 valuable reference to the Dirac operator and its applications in theoretical physics.
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Book DetailsISBN: 9780521648622
(228mm x 152mm x 13mm)
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 20-Aug-1998
Country of Publication: United Kingdom
Books By Author Giampiero Esposito
Advanced Concepts in Quantum Mechanics, Hardback (November 2014)
This book introduces a geometric view of fundamental physics, ideal for advanced undergraduate and graduate students in quantum mechanics and mathematical physics.
From Classical to Quantum Mechanics, Paperback (June 2010)
This 2004 textbook provides a pedagogical introduction to the formalism, foundations and applications of quantum mechanics.
Quantum Gravity in Four Dimensions, Hardback (September 2001)» View all books by Giampiero Esposito
Main section headings: Ideas and Problems in Quantum Gravity; On Ellipticity and Quantum Gravity; Non-Local Boundary Data in Quantum Gravity; Non-Locality and Ellipticity for Gauge Theories; New Kernels in Quantum Gravity; Quantum Gravity from First Principles; Quantum Gravity and Spectral Geometry; Bibliography; Index.
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