This textbook provides a pedagogical introduction to the formalism, foundations and applications of quantum mechanics. Part I covers the basic material which is necessary to understand the transition from classical to wave mechanics. Topics include classical dynamics, with emphasis on canonical transformations and the Hamilton-Jacobi equation, the ...
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 non-local boundary conditions. The theory is introduced at a level suitable for graduate ...
This volume introduces the application of two-component spinor calculus and fibre-bundle theory to complex general relativity. A review of basic and important topics is presented, such as two-component spinor calculus, conformal gravity, twistor spaces for Minkowski space-time and for curved space-time, Penrose transform for gravitation, the ...
All papers were peer reviewed. Research advances in gravitation and general relativity are discussed, ranging from classical to quantum theories of gravity. Relativistic theories have become the basic model for new research fields encompassing importantexperiments and observations which represent a frontier on which Einstein's theory of gravity ...
Beginning with a review of the physical and mathematical motivations for studying physical theories in the presence of boundaries, this text places emphasis on electrostatics, vacuum Maxwell theory and quantum cosmology. The Feynman propagator is then studied in Minkowski space-time and in curved space-time. In the latter case, the corresponding ...
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.
The first aim of this book is to describe recent work on the problem of boundary conditions in one-loop quantum cosmology. The motivation is to understand whether supersymmetric theories are one-loop finite in the presence of boundaries. The second aim of the book is to present a recent, entirely new study of the singularity problem for space ...
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