Euclidean Quantum Gravity On Manifolds With Boundary

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Euclidean Quantum Gravity on Manifolds with Boundary

Author : Giampiero Esposito
Publisher : Springer Science & Business Media
ISBN 13 : 9401158061
Total Pages : 334 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Euclidean Quantum Gravity on Manifolds with Boundary by : Giampiero Esposito

Download or read book Euclidean Quantum Gravity on Manifolds with Boundary written by Giampiero Esposito and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds

Author : Krzysztof P. Wojciechowski
Publisher : American Mathematical Soc.
ISBN 13 : 082183536X
Total Pages : 338 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds by : Krzysztof P. Wojciechowski

Download or read book Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds written by Krzysztof P. Wojciechowski and published by American Mathematical Soc.. This book was released on 2005 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 theory of spectral invariants on closed manifolds and manifolds with 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 traces, indices, and determinants. Part III is concerned with general 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.

Quantum Gravity in Four Dimensions

Author : Giampiero Esposito
Publisher : Nova Publishers
ISBN 13 : 9781590330005
Total Pages : 176 pages
Book Rating : 4.3/5 (3 download)

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Book Synopsis Quantum Gravity in Four Dimensions by : Giampiero Esposito

Download or read book Quantum Gravity in Four Dimensions written by Giampiero Esposito and published by Nova Publishers. This book was released on 2001 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Analysis, Geometry and Topology of Elliptic Operators

Author : Bernhelm Booss
Publisher : World Scientific
ISBN 13 : 9812773606
Total Pages : 553 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Analysis, Geometry and Topology of Elliptic Operators by : Bernhelm Booss

Download or read book Analysis, Geometry and Topology of Elliptic Operators written by Bernhelm Booss and published by World Scientific. This book was released on 2006 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Analysis, Geometry And Topology Of Elliptic Operators: Papers In Honor Of Krzysztof P Wojciechowski

Author : Matthias Lesch
Publisher : World Scientific
ISBN 13 : 9814478024
Total Pages : 553 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Analysis, Geometry And Topology Of Elliptic Operators: Papers In Honor Of Krzysztof P Wojciechowski by : Matthias Lesch

Download or read book Analysis, Geometry And Topology Of Elliptic Operators: Papers In Honor Of Krzysztof P Wojciechowski written by Matthias Lesch and published by World Scientific. This book was released on 2006-04-25 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Quantum Gravity, Quantum Cosmology and Lorentzian Geometries

Author : Giampiero Esposito
Publisher : Springer Science & Business Media
ISBN 13 : 3540472959
Total Pages : 364 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Quantum Gravity, Quantum Cosmology and Lorentzian Geometries by : Giampiero Esposito

Download or read book Quantum Gravity, Quantum Cosmology and Lorentzian Geometries written by Giampiero Esposito and published by Springer Science & Business Media. This book was released on 2009-02-13 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is aimed at theoretical and mathematical physicists and mathematicians interested in modern gravitational physics. I have thus tried to use language familiar to readers working on classical and quantum gravity, paying attention both to difficult calculations and to existence theorems, and discussing in detail the current literature. The first aim of the book is to describe recent work on the problem of boundary conditions in one-loop quantum cosmology. The motivation of this research was to under stand whether supersymmetric theories are one-loop finite in the presence of boundaries, with application to the boundary-value problemsoccurring in quantum cosmology. Indeed, higher-loop calculations in the absence of boundaries are already available in the litera ture, showing that supergravity is not finite. I believe, however, that one-loop calculations in the presence of boundaries are more fundamental, in that they provide a more direct check of the inconsistency of supersymmetric quantum cosmology from the perturbative point of view. It therefore appears that higher-order calculations are not strictly needed, if the one-loop test already yields negative results. Even though the question is not yet settled, this research has led to many interesting, new applications of areas of theoretical and mathematical physics such as twistor theory in flat space, self-adjointness theory, the generalized Riemann zeta-function, and the theory of boundary counterterms in super gravity. I have also compared in detail my work with results by other authors, explaining, whenever possible, the origin of different results, the limits of my work and the unsolved problems.

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

Download Casimir Effect 50 Years Later,the - Proceedings Of The Fourth Workshop On Quantum Field Theory Under The Influence Of External Conditions PDF Online Free

Author : Michael Bordag
Publisher : World Scientific
ISBN 13 : 9814543853
Total Pages : 410 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Casimir Effect 50 Years Later,the - Proceedings Of The Fourth Workshop On Quantum Field Theory Under The Influence Of External Conditions by : Michael Bordag

Download or read book 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 published by World Scientific. This book was released on 1999-04-01 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Geometrical Aspects of Quantum Fields

Author : Andrei A. Bytsenko
Publisher : World Scientific
ISBN 13 : 9810245025
Total Pages : 213 pages
Book Rating : 4.8/5 (12 download)

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Book Synopsis Geometrical Aspects of Quantum Fields by : Andrei A. Bytsenko

Download or read book Geometrical Aspects of Quantum Fields written by Andrei A. Bytsenko and published by World Scientific. This book was released on 2001 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Asymptotic Formulae in Spectral Geometry

Author : Peter B. Gilkey
Publisher : CRC Press
ISBN 13 : 1135440743
Total Pages : 315 pages
Book Rating : 4.1/5 (354 download)

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Book Synopsis Asymptotic Formulae in Spectral Geometry by : Peter B. Gilkey

Download or read book Asymptotic Formulae in Spectral Geometry written by Peter B. Gilkey and published by CRC Press. This book was released on 2003-12-17 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

The Universality of Physics

Author : Ramzi R. Khuri
Publisher : Springer Science & Business Media
ISBN 13 : 1461505852
Total Pages : 199 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis The Universality of Physics by : Ramzi R. Khuri

Download or read book The Universality of Physics written by Ramzi R. Khuri and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Quantum Field Theory and Gravity

Author : Felix Finster
Publisher : Springer Science & Business Media
ISBN 13 : 3034800436
Total Pages : 382 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Quantum Field Theory and Gravity by : Felix Finster

Download or read book Quantum Field Theory and Gravity written by Felix Finster and published by Springer Science & Business Media. This book was released on 2012-02-08 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most challenging problems of contemporary theoretical physics is the mathematically rigorous construction of a theory which describes gravitation and the other fundamental physical interactions within a common framework. The physical ideas which grew from attempts to develop such a theory require highly advanced mathematical methods and radically new physical concepts. This book presents different approaches to a rigorous unified description of quantum fields and gravity. It contains a carefully selected cross-section of lively discussions which took place in autumn 2010 at the fifth conference "Quantum field theory and gravity - Conceptual and mathematical advances in the search for a unified framework" in Regensburg, Germany. In the tradition of the other proceedings covering this series of conferences, a special feature of this book is the exposition of a wide variety of approaches, with the intention to facilitate a comparison. The book is mainly addressed to mathematicians and physicists who are interested in fundamental questions of mathematical physics. It allows the reader to obtain a broad and up-to-date overview of a fascinating active research area.

Spectral Functions in Mathematics and Physics

Author : Klaus Kirsten
Publisher : CRC Press
ISBN 13 : 1420035460
Total Pages : 397 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Spectral Functions in Mathematics and Physics by : Klaus Kirsten

Download or read book Spectral Functions in Mathematics and Physics written by Klaus Kirsten and published by CRC Press. This book was released on 2001-12-13 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Bernhelm Booss
Publisher : American Mathematical Soc.
ISBN 13 : 9780821857007
Total Pages : 340 pages
Book Rating : 4.8/5 (57 download)

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Book Synopsis Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds by : Bernhelm Booss

Download or read book Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds written by Bernhelm Booss and published by American Mathematical Soc.. This book was released on 2005-01-05 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 range from spectral flow calculations and cut-and-paste considerations, via pseudodifferential methods, asymptotic expansions and variational arguments, to singular manifold theories and $K$-theoretic cohomological strategies. They lead to results on determinants, heat kernels, general trace, index and higher signature formulas, low-dimensional topological invariants, as well as on the structure of the manifolds and operators involved. Moreover, the approaches and results are placed in a physics context by two reviews on the applications in quantum field theory, respectively quantum gravity. This book is suitable for graduate students and researchers interested in spectral problems in geometry.

Dirac Operators and Spectral Geometry

Author : Giampiero Esposito
Publisher : Cambridge University Press
ISBN 13 : 0521648629
Total Pages : 227 pages
Book Rating : 4.5/5 (216 download)

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Book Synopsis Dirac Operators and Spectral Geometry by : Giampiero Esposito

Download or read book Dirac Operators and Spectral Geometry written by Giampiero Esposito and published by Cambridge University Press. This book was released on 1998-08-20 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Operators, Geometry and Quanta

Author : Dmitri Fursaev
Publisher : Springer Science & Business Media
ISBN 13 : 9400702051
Total Pages : 294 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis Operators, Geometry and Quanta by : Dmitri Fursaev

Download or read book Operators, Geometry and Quanta written by Dmitri Fursaev and published by Springer Science & Business Media. This book was released on 2011-06-25 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a detailed and self-contained introduction into the theory of spectral functions, with an emphasis on their applications to quantum field theory. All methods are illustrated with applications to specific physical problems from the forefront of current research, such as finite-temperature field theory, D-branes, quantum solitons and noncommutativity. In the first part of the book, necessary background information on differential geometry and quantization, including less standard material, is collected. The second part of the book contains a detailed description of main spectral functions and methods of their calculation. In the third part, the theory is applied to several examples (D-branes, quantum solitons, anomalies, noncommutativity). This book addresses advanced graduate students and researchers in mathematical physics with basic knowledge of quantum field theory and differential geometry. The aim is to prepare readers to use spectral functions in their own research, in particular in relation to heat kernels and zeta functions.

Euclidean Quantum Gravity

Author : G. W. Gibbons
Publisher : World Scientific
ISBN 13 : 9789810205164
Total Pages : 604 pages
Book Rating : 4.2/5 (51 download)

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Book Synopsis Euclidean Quantum Gravity by : G. W. Gibbons

Download or read book Euclidean Quantum Gravity written by G. W. Gibbons and published by World Scientific. This book was released on 1993 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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: Proceedings Of The Sixth Moscow Quantum Gravity Seminar

Author : V A Berezin
Publisher : World Scientific
ISBN 13 : 9814546305
Total Pages : 666 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Quantum Gravity: Proceedings Of The Sixth Moscow Quantum Gravity Seminar by : V A Berezin

Download or read book Quantum Gravity: Proceedings Of The Sixth Moscow Quantum Gravity Seminar written by V A Berezin and published by World Scientific. This book was released on 1998-03-09 with total page 666 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Sixth Moscow Quantum Gravity Seminar was a continuation of the series of seminars which has played an important role in the consolidation of the international quantum gravity community and which has greatly affected the development of the field. As well as papers presented at the conference, this proceedings volume includes the papers of invited speakers who were unable to attend the seminar itself.