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Euclidean Quantum Gravity On Manifolds With Boundary

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Euclidean Quantum Gravity On Manifolds With Boundary

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Author : Maria Rosaria D'Esposito
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-03-31

Euclidean Quantum Gravity On Manifolds With Boundary written by Maria Rosaria D'Esposito and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-03-31 with Science categories.

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.

Euclidean Quantum Gravity On Manifolds With Boundary

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Author : Giampiero Esposito
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Euclidean Quantum Gravity On Manifolds With Boundary written by Giampiero Esposito and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.

Spectral Geometry Of Manifolds With Boundary And Decomposition Of Manifolds

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Author : Gerd Grubb
language : en
Publisher: American Mathematical Soc.
Release Date : 2005

Spectral Geometry Of Manifolds With Boundary And Decomposition Of Manifolds written by Gerd Grubb and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.

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.

Euclidean Quantum Gravity

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Author : G. W. Gibbons
language : en
Publisher: World Scientific
Release Date : 1993

Euclidean Quantum Gravity written by G. W. Gibbons and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Science categories.

The Euclidean approach to Quantum Gravity was initiated almost 15 years ago in an attempt to understand the difficulties raised by the spacetime singularities of classical general relativity which arise in the gravitational collapse of stars to form black holes and the entire universe in the Big Bang. An important motivation was to develop an approach capable of dealing with the nonlinear, non-perturbative aspects of quantum gravity due to topologically non-trivial spacetimes. There are important links with a Riemannian geometry. Since its inception the theory has been applied to a number of important physical problems including the thermodynamic properties of black holes, quantum cosmology and the problem of the cosmological constant. It is currently at the centre of a great deal of interest.This is a collection of survey lectures and reprints of some important lectures on the Euclidean approach to quantum gravity in which one expresses the Feynman path integral as a sum over Riemannian metrics. As well as papers on the basic formalism there are sections on Black Holes, Quantum Cosmology, Wormholes and Gravitational Instantons.

Quantum Gravity In Four Dimensions

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Author : Giampiero Esposito
language : en
Publisher: Nova Publishers
Release Date : 2001

Quantum Gravity In Four Dimensions written by Giampiero Esposito and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Science categories.

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.

Geometrical Aspects Of Quantum Fields Proceedings Of The 2000 Londrina Workshop

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Author : Andrei A Bytsenko
language : en
Publisher: World Scientific
Release Date : 2001-02-05

Geometrical Aspects Of Quantum Fields Proceedings Of The 2000 Londrina Workshop written by Andrei A Bytsenko and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-02-05 with Science categories.

This volume presents the following topics: non-Abelian Toda models, brief remarks for physicists on equivariant cohomology and the Duistermaat-Heckman formula, Casimir effect, quantum groups and their application to nuclear physics, quantum field theory, quantum gravity and the theory of extended objects, and black hole physics and cosmology.

Casimir Effect 50 Years Later The Proceedings Of The Fourth Workshop On Quantum Field Theory Under The Influence Of External Conditions

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Author : Michael Bordag
language : en
Publisher: World Scientific
Release Date : 1999-04-01

Casimir Effect 50 Years Later The Proceedings Of The Fourth Workshop On Quantum Field Theory Under The Influence Of External Conditions written by Michael Bordag and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-04-01 with categories.

This volume contains papers based on talks delivered at the Fourth Workshop on Quantum Field Theory Under the Influence of External Conditions. This series of workshops, held at the Institute for Theoretical Physics of the University of Leipzig, was launched in 1989. The present meeting took place 50 years after Hendrik B Casimir discovered the effect named after him. This effect was found by Casimir in investigating the retarded long range van der Waals forces in colloids and re-expressing them as a change in the vacuum energy of the electromagnetic field. The story of why this work was done was told by Casimir himself at the workshop. A historical account of the development of vacuum energy in quantum theory starting from Planck's half quanta was given by H Rechenberg. Another interesting topic was about a possible explanation of sonoluminescence as a dynamical Casimir effect. Kim Milton reported on the work done by Julian Schwinger on this topic during the last years of the great physicist's life, as well as on his own research. M Bordag (Leipzig) provided a general analysis of the ultraviolet divergences of the vacuum energy of a dielectric sphere.The Casimir effect had been experimentally verified 10 years after its discovery on a rather qualitative level. Only last year and in another experiment this year, it became also quantitatively well established. It turned out to be of unexpectedly high sensitivity with respect to the presence of the so-called fifth forces, as V Mostepanenko showed in his talk.Modern methods of computing the Casimir effect rely on zeta functional regularization and heat kernel expansion. This mathematical background, together with a broader embedding into expansions of various spectral quantities, was the subject of the talk by S Fulling. Recent progress in the computation of the heat kernel coefficients was reported by V Kornyak and K Kirsten.A number of talks were devoted to magnetic background fields of various types; for instance, new trends in the Aharonov-Bohm effect. In cosmology, negative energy densities and the role of adiabatic vacuum states in a de Sitter universe were discussed.

Asymptotic Formulae In Spectral Geometry

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Author : Peter B. Gilkey
language : en
Publisher: CRC Press
Release Date : 2003-12-17

Asymptotic Formulae In Spectral Geometry written by Peter B. Gilkey and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-17 with Mathematics categories.

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 to be the definitive book on the subject.

Analysis Geometry And Topology Of Elliptic Operators

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Author : Bernhelm Booss
language : en
Publisher: World Scientific
Release Date : 2006

Analysis Geometry And Topology Of Elliptic Operators written by Bernhelm Booss and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.

Modern theory of elliptic operators, or simply elliptic theory, has been shaped by the Atiyah-Singer Index Theorem created 40 years ago. Reviewing elliptic theory over a broad range, 32 leading scientists from 14 different countries present recent developments in topology; heat kernel techniques; spectral invariants and cutting and pasting; noncommutative geometry; and theoretical particle, string and membrane physics, and Hamiltonian dynamics. The first of its kind, this volume is ideally suited to graduate students and researchers interested in careful expositions of newly-evolved achievements and perspectives in elliptic theory. The contributions are based on lectures presented at a workshop acknowledging Krzysztof P Wojciechowski''s work in the theory of elliptic operators. Sample Chapter(s). Contents (42 KB). Contents: On the Mathematical Work of Krzysztof P Wojciechowski: Selected Aspects of the Mathematical Work of Krzysztof P Wojciechowski (M Lesch); Gluing Formulae of Spectral Invariants and Cauchy Data Spaces (J Park); Topological Theories: The Behavior of the Analytic Index under Nontrivial Embedding (D Bleecker); Critical Points of Polynomials in Three Complex Variables (L I Nicolaescu); Chern-Weil Forms Associated with Superconnections (S Paycha & S Scott); Heat Kernel Calculations and Surgery: Non-Laplace Type Operators on Manifolds with Boundary (I G Avramidi); Eta Invariants for Manifold with Boundary (X Dai); Heat Kernels of the Sub-Laplacian and the Laplacian on Nilpotent Lie Groups (K Furutani); Remarks on Nonlocal Trace Expansion Coefficients (G Grubb); An Anomaly Formula for L 2- Analytic Torsions on Manifolds with Boundary (X Ma & W Zhang); Conformal Anomalies via Canonical Traces (S Paycha & S Rosenberg); Noncommutative Geometry: An Analytic Approach to Spectral Flow in von Neumann Algebras (M-T Benameur et al.); Elliptic Operators on Infinite Graphs (J Dodziuk); A New Kind of Index Theorem (R G Douglas); A Note on Noncommutative Holomorphic and Harmonic Functions on the Unit Disk (S Klimek); Star Products and Central Extensions (J Mickelsson); An Elementary Proof of the Homotopy Equivalence between the Restricted General Linear Group and the Space of Fredholm Operators (T Wurzbacher); Theoretical Particle, String and Membrane Physics, and Hamiltonian Dynamics: T-Duality for Non-Free Circle Actions (U Bunke & T Schick); A New Spectral Cancellation in Quantum Gravity (G Esposito et al.); A Generalized Morse Index Theorem (C Zhu). Readership: Researchers in modern global analysis and particle physics.

Recent Developments In General Relativity Genoa 2000

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Author : R. Cianci
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Recent Developments In General Relativity Genoa 2000 written by R. Cianci and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Science categories.

A survey of the most recent developments in general relativity and in the theory of the unification of Fundamental Interactions is presented in this book. The theoretical results, the cosmological and astrophysical aspects, the experimental and observational programs are shown in 26 general talks by renowned scientists active in this field.

Euclidean Quantum Gravity On Manifolds With Boundary

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