Euclidean Quantum Gravity on Manifolds with Boundary

Euclidean Quantum Gravity on Manifolds with Boundary
Title Euclidean Quantum Gravity on Manifolds with Boundary PDF eBook
Author Giampiero Esposito
Publisher Springer Science & Business Media
Pages 334
Release 2012-12-06
Genre Science
ISBN 9401158061

Download Euclidean Quantum Gravity on Manifolds with Boundary Book in PDF, Epub and Kindle

This book reflects our own struggle to understand the semiclassical behaviour of quantized fields in the presence of boundaries. Along many years, motivated by the problems of quantum cosmology and quantum field theory, we have studied in detail the one-loop properties of massless spin-l/2 fields, Euclidean Maxwell the ory, gravitino potentials and Euclidean quantum gravity. Hence our book begins with a review of the physical and mathematical motivations for studying physical theories in the presence of boundaries, with emphasis on electrostatics, vacuum v Maxwell theory and quantum cosmology. We then study the Feynman propagator in Minkowski space-time and in curved space-time. In the latter case, the corre sponding Schwinger-DeWitt asymptotic expansion is given. The following chapters are devoted to the standard theory of the effective action and the geometric im provement due to Vilkovisky, the manifestly covariant quantization of gauge fields, zeta-function regularization in mathematics and in quantum field theory, and the problem of boundary conditions in one-loop quantum theory. For this purpose, we study in detail Dirichlet, Neumann and Robin boundary conditions for scalar fields, local and non-local boundary conditions for massless spin-l/2 fields, mixed boundary conditions for gauge fields and gravitation. This is the content of Part I. Part II presents our investigations of Euclidean Maxwell theory, simple super gravity and Euclidean quantum gravity.

Asymptotic Formulae in Spectral Geometry

Asymptotic Formulae in Spectral Geometry
Title Asymptotic Formulae in Spectral Geometry PDF eBook
Author Peter B. Gilkey
Publisher CRC Press
Pages 315
Release 2003-12-17
Genre Mathematics
ISBN 1135440743

Download Asymptotic Formulae in Spectral Geometry Book in PDF, Epub and Kindle

A great deal of progress has been made recently in the field of asymptotic formulas that arise in the theory of Dirac and Laplace type operators. Asymptotic Formulae in Spectral Geometry collects these results and computations into one book. Written by a leading pioneer in the field, it focuses on the functorial and special cases methods of computing asymptotic heat trace and heat content coefficients in the heat equation. It incorporates the work of many authors into the presentation, and includes a complete bibliography that serves as a roadmap to the literature on the subject. Geometers, mathematical physicists, and analysts alike will undoubtedly find this book to be the definitive book on the subject

Quantum Gravity in Four Dimensions

Quantum Gravity in Four Dimensions
Title Quantum Gravity in Four Dimensions PDF eBook
Author Giampiero Esposito
Publisher Nova Publishers
Pages 176
Release 2001
Genre Science
ISBN 9781590330005

Download Quantum Gravity in Four Dimensions Book in PDF, Epub and Kindle

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 Universality of Physics

The Universality of Physics
Title The Universality of Physics PDF eBook
Author Ramzi R. Khuri
Publisher Springer Science & Business Media
Pages 199
Release 2012-12-06
Genre Science
ISBN 1461505852

Download The Universality of Physics Book in PDF, Epub and Kindle

Deng Feng Wang was born February 8, 1965 in Chongqing City, China and died August 15, 1999 while swimming with friends in the Atlantic Ocean off Island Beach State Park, New Jersey. In his brief life, he was to have an influence far beyond his years. On August 12th 2000, The Deng Feng Wang Memorial Conference was held at his alma mater, Princeton University, during which Deng Feng's mentors, collaborators and friends presented scientific talks in a testimonial to his tremendous influence on their work and careers. The first part of this volume contains proceedings contributions from the conference, with plenary talks by Nobel Laureate Professor Phil Anderson of Princeton University and leading Condensed Matter Theorists Professor Piers Coleman of Rutgers University and Professor Christian Gruber of the University of Lausanne. Other talks, given by collaborators, friends and classmates testify to the great breadth of Deng Feng Wang's influence, with remarkable connections shown between seemingly unrelated areas in physics such as Condensed Matter Physics, Superconductivity, One-Dimensional Models, Statistical Physics, Mathematical Physics, Quantum Field Theory, High Energy Theory, Nuclear Magnetic Resonance, Supersymmetry, M-Theory and String Theory, in addition to such varied fields outside of physics such as Oil Drilling, Mixed Signal Circuits and Neurology. The second part of the volume consists of reprints of some of Deng Feng Wang's most important papers in the areas of Condensed Matter Physics, Statistical Physics, Magnetism, Mathematical Physics and Mathematical Finance. This volume represents a fascinating synthesis of a wide variety of topics, and ultimately points to the universality of physics and of science as a whole. As such, it represents a fitting tribute to a remarkable individual, whose tragic death will never erase his enduring influence.

Spectral Functions in Mathematics and Physics

Spectral Functions in Mathematics and Physics
Title Spectral Functions in Mathematics and Physics PDF eBook
Author Klaus Kirsten
Publisher CRC Press
Pages 349
Release 2001-12-13
Genre Mathematics
ISBN 1000738159

Download Spectral Functions in Mathematics and Physics Book in PDF, Epub and Kindle

The literature on the spectral analysis of second order elliptic differential operators contains a great deal of information on the spectral functions for explicitly known spectra. The same is not true, however, for situations where the spectra are not explicitly known. Over the last several years, the author and his colleagues have developed new,

Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds

Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds
Title Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds PDF eBook
Author Gerd Grubb
Publisher American Mathematical Soc.
Pages 338
Release 2005
Genre Mathematics
ISBN 082183536X

Download Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds Book in PDF, Epub and Kindle

In recent years, increasingly complex methods have been brought into play in the treatment of geometric and topological problems for partial differential operators on manifolds. This collection of papers, resulting from a Workshop on Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds, provides a broad picture of these methods with new results. Subjects in the book cover a wide variety of topics, from recent advances in index theory and the more general boundary, to applications of those invariants in geometry, topology, and physics. Papers are grouped into four parts: Part I gives an overview of the subject from various points of view. Part II deals with spectral invariants, such as geometric and topological questions. Part IV deals specifically with problems on manifolds with singularities. The book is suitable for graduate students and researchers interested in spectral problems in geometry.

Dirac Operators and Spectral Geometry

Dirac Operators and Spectral Geometry
Title Dirac Operators and Spectral Geometry PDF eBook
Author Giampiero Esposito
Publisher Cambridge University Press
Pages 227
Release 1998-08-20
Genre Mathematics
ISBN 0521648629

Download Dirac Operators and Spectral Geometry Book in PDF, Epub and Kindle

A clear, concise and up-to-date introduction to the theory of the Dirac operator and its wide range of applications in theoretical physics for graduate students and researchers.