## The Quantization of Gravity

Author: Claus Gerhardt

Publisher: Springer

ISBN: 3319773712

Category: Science

Page: 200

View: 9572

​A unified quantum theory incorporating the four fundamental forces of nature is one of the major open problems in physics. The Standard Model combines electro-magnetism, the strong force and the weak force, but ignores gravity. The quantization of gravity is therefore a necessary first step to achieve a unified quantum theory. In this monograph a canonical quantization of gravity has been achieved by quantizing a geometric evolution equation resulting in a gravitational wave equation in a globally hyperbolic spacetime. Applying the technique of separation of variables we obtain eigenvalue problems for temporal and spatial self-adjoint operators where the temporal operator has a pure point spectrum with eigenvalues $\lambda_i$ and related eigenfunctions, while, for the spatial operator, it is possible to find corresponding eigendistributions for each of the eigenvalues $\lambda_i$, if the Cauchy hypersurface is asymptotically Euclidean or if the quantized spacetime is a black hole with a negative cosmological constant. The hyperbolic equation then has a sequence of smooth solutions which are products of temporal eigenfunctions and spatial eigendistributions. Due to this "spectral resolution" of the wave equation quantum statistics can also be applied to the quantized systems. These quantum statistical results could help to explain the nature of dark matter and dark energy.

## Quantum Gravity

Author: Marlys Staudt

Publisher: OUP Oxford

ISBN: 0191607401

Category: Science

Page: 376

View: 7527

The search for a quantum theory of the gravitational field is one of the great open problems in theoretical physics. This book presents a self-contained discussion of the concepts, methods and applications that can be expected in such a theory. The two main approaches to its construction -- the direct quantisation of Einstein's general theory of relativity and string theory -- are covered. Whereas the first attempts to construct a viable theory for the gravitational field alone,string theory assumes that a quantum theory of gravity will be achieved only through a unification of all the interactions. However, both employ the general method of quantization of constrained systems, which is described together with illustrative examples relevant for quantum gravity. There is adetailed presentation of the main approaches employed in quantum general relativity: path-integral quantization, the background-field method and canonical quantum gravity in the metric, connection and loop formulations. The discussion of string theory centres around its quantum-gravitational aspects and the comparison with quantum general relativity. Physical applications discussed at length include the quantization of black holes, quantum cosmology, the indications of a discrete structure ofspacetime, and the origin of irreversibility.The second edition will add some sections on topical issues. These include loop quantum cosmology, dynamical triangulation, renormalization-group approach, primordial black holes, and information-loss problem for black holes. The second edition will also contain some pedagogical extensions.This book will be of interest to researchers and students working in relativity and gravitation, cosmology, quantum field theory and related topics. It will also be of interest to mathematicians and philosophers of science.

## Quantum Gravity

Third Edition

Author: Claus Kiefer

Publisher: Oxford University Press

ISBN: 0199585202

Category: Mathematics

Page: 393

View: 7921

Quantum theory and Einstein's theory of relativity are at the centre of modern theoretical physics, yet, the consistent unification of both theories is still elusive. This book offers an up-to-date introduction into the attempts to construct a unified theory of "quantum gravity".

## Quantization of Singular Symplectic Quotients

Author: N.P. Landsman,Markus Pflaum,Martin Schlichenmaier

Publisher: Birkhäuser

ISBN: 3034883641

Category: Mathematics

Page: 355

View: 3839

This is the first exposition of the quantization theory of singular symplectic (Marsden-Weinstein) quotients and their applications to physics. The reader will acquire an introduction to the various techniques used in this area, as well as an overview of the latest research approaches. These involve classical differential and algebraic geometry, as well as operator algebras and noncommutative geometry. Thus one will be amply prepared to follow future developments in this field.

## The Meaning of Quantum Gravity

Author: Horst-Heino Borzeszkowski,H.J. Treder

Publisher: Springer Science & Business Media

ISBN: 9400938934

Category: Science

Page: 132

View: 9251

In discussing the question of whether General Relativity Theory really needs to be quantized, a simply negative answer cannot be accepted, of course. Such an answer is not satisfying because, first, Einstein's gravitational equations connect gravity and non-gravitational matter and because, second, it can be taken for granted that non-gravitational matter has an atomic or quantum structure such that its energy-momentum tensor standing on the right-hand side of Einstein's equations is formed out of quantum operators. These two facts make it impossible to read the left-hand side of Einstein's equations as an ordinary classical function. This does not necessarily mean, however, that we must draw the conclusion that General Relativity Theory, similar to electrodynamics, could or should be quantized in a rigorous manner and that this quantization has similar consequences to quantum electrodynamics. In other words, when for reasons of consistency quantization is tried, then one has to ask whether and where the quantization procedure has a physical meaning, i.e., whether there exist measurable effects of quantum gravity. IQ accordance with these questions, we are mainly dealing with the discus sion of the principles of quantized General Relativity Theory and with the estimation of quantum effects including the question of their measurability. This analysis proves that it is impossible to distinguish between classical and quantum General Relativity Theory for the extreme case of Planck's orders of magnitude. In other words, there does not exist a physically meaningful rigorous quantization conception for Einstein's theory.

## Quantum Gravity in 2+1 Dimensions

Author: Steven Carlip,Steven Jonathan Carlip

Publisher: Cambridge University Press

ISBN: 9780521545884

Category: Science

Page: 276

View: 8057

The first comprehensive survey of (2+1)-dimensional quantum gravity - for graduate students and researchers.

## Foundations of Space and Time

Reflections on Quantum Gravity

Author: Jeff Murugan,Amanda Weltman,George F. R. Ellis

Publisher: Cambridge University Press

ISBN: 0521114403

Category: Science

Page: 437

View: 6754

Encapsulates the latest debates on this topic, giving researchers and graduate students an up-to-date view of the field.

## Quantum Fluctuations of Spacetime

Author: Lawrence B. Crowell

Publisher: World Scientific

ISBN: 9812565159

Category: Science

Page: 373

View: 8412

Three key aspects of quantum gravity are considered in this book: phenomenology, potential experimental aspects and foundational theory. The phenomenology is the treatment of metric quantum fluctuations as torsional curves that deviate from classical expectations. This leads to possible experimental configurations that may detect such fluctuations. Most of these proposed experiments are quantum optical measurements of subtle quantum gravity effects in the interaction of photons and atoms. The foundational discussions attempt to find an substratum to string theories, which are motivated by the phenomenological treatment. Quantum gravity is not the quantization of general relativity, but is instead the embedding of quantum theory and gravitation into a more fundamental field theoretic framework.

## The Pursuit of Quantum Gravity

Memoirs of Bryce DeWitt from 1946 to 2004

Author: Cécile DeWitt-Morette

Publisher: Springer Science & Business Media

ISBN: 9783642142703

Category: Science

Page: 151

View: 1827

1946 is the year Bryce DeWitt entered Harvard graduate school. Quantum Gravity was his goal and remained his goal throughout his lifetime until the very end. The pursuit of Quantum Gravity requires a profound understanding of Quantum Physics and Gravitation Physics. As G. A. Vilkovisky commented , "Quantum Gravity is a combination of two words, and one should know both. Bryce understood this as nobody else, and this wisdom is completely unknown to many authors of the flux of papers that we see nowadays." Distingished physicist Cecile DeWitt-Morette skillfully blends her personal and scientific account with a wealth of her late husband's often unpublished writings on the subject matter. This volume, through the perspective of the leading researcher on quantum gravity of his generation, will provide an invaluable source of reference for anyone working in the field.

## Experimental Search for Quantum Gravity

Author: Sabine Hossenfelder

Publisher: Springer

ISBN: 3319645374

Category: Science

Page: 120

View: 1682

This book summarizes recent developments in the research area of quantum gravity phenomenology. A series of short and nontechnical essays lays out the prospects of various experimental possibilities and their current status. Finding observational evidence for the quantization of space-time was long thought impossible. In the last decade however, new experimental design and technological advances have changed the research landscape and opened new perspectives on quantum gravity. Formerly dominated by purely theoretical constructions, quantum gravity now has a lively phenomenology to offer. From high precision measurements using macroscopic quantum oscillators to new analysis methods of the cosmic microwave background, no stone is being left unturned in the experimental search for quantum gravity. This book sheds new light on the connection of astroparticle physics with the quantum gravity problem. Gravitational waves and their detection are covered. It illustrates findings from the interconnection between general relativity, black holes and Planck stars. Finally, the return on investment in quantum-gravitation research is illuminated. The book is intended for graduate students and researchers entering the field.

## Approaches to Quantum Gravity

Toward a New Understanding of Space, Time and Matter

Author: Daniele Oriti

Publisher: Cambridge University Press

ISBN: 0521860458

Category: Science

Page: 583

View: 4882

Containing contributions from leading researchers in this field, this book provides a complete overview of this field from the frontiers of theoretical physics research for graduate students and researchers. It introduces the most current approaches to this problem, and reviews their main achievements.

## Introduction to Quantum Effects in Gravity

Author: Viatcheslav Mukhanov,Sergei Winitzki

Publisher: Cambridge University Press

ISBN: 9780521868341

Category: Mathematics

Page: 273

View: 7450

This book, first published in 2007, cover quantum field theory for undergraduates and graduates in theoretical astrophysics, cosmology, particle physics, and string theory.

## Advances in the Interplay Between Quantum and Gravity Physics

Author: Peter G. Bergmann,V. de Sabbata

Publisher: Springer Science & Business Media

ISBN: 9781402005923

Category: Science

Page: 554

View: 5676

In this XVII Course of the International School of Cosmology and Gravitation devoted to "ADVANCES IN THE INTERPLAY BETWEEN QUANTUM AND GRAVITY PHYSICS" we have considered different aspects of the influence of gravity on quantum systems. In order to achieve this aim, in many lectures, seminars and discussions we have strengthened the interplay between gravity and quantum systems starting from the situation in the early universe based on astrophysical observations, up to the earthly based experiments with atom interferometry for probing the structure of space-time. Thus we have had timely lectures on the quantum field and horizon of a black hole including reviews of the problem of black holes thermodynamics and entropy, quantum information, quantum black holes, quantum evaporation and Hawking radiation, recent advances in stockastic gravity. We have also discussed quantum fluctuations in inflationary universe, quantum effects and reheating after inflation, and superplanckian energies in Hawking radiation. In this regard the subject of spinors in purely affine space-time and Dirac matter according to Weyl in the generalized theory of gravitation were developed . The dualism between space-time and matter has been deeply analyzed in order to see why, for general relativity, this is an obstacle for quantization of the theory. Also canonical Gravity and Mach's principle, torsion and curvature as commutator for Quantum Gravity and Dirac Geometry of real space-time were analysed, together with the problem of 5-Dimensional Projective Unified Field theory and Multidimensional Gravity and Cosmology.

## Quantum Gravity

Author: M. Markov

Publisher: Springer Science & Business Media

ISBN: 1461327016

Category: Science

Page: 548

View: 2208

Three years have passed after the First Moscow Seminar on Quantum Gravity. It is a rather long time interval for the modern theoretical physics. The talks given at the present Second Seminar which took place in October 13-15, 1981 in Moscow contain the discussion of new results obtained during this period and the problems which arose. More than one hundred Soviet scientists and a number of the foreign guests attended this Seminar, which as the previous one was held by the Nuclear Physics Department of the Academy of Sciences of the USSR and the Institute for Nuclear Research of the Academy of Sciences of the USSR. The aim of the Seminar was to discuss the most important problems of the modern Quantum Gravity, namely: i) Quantum Gravity: the state of art; ii) Quantum effects in Cosmology; iii) Quantum black-hole physics; iv) the recent development in Supergravity and v) Quantum Gauge Theories. The Editorial Board expresses its sincere gratitude to all physicists who have contributed to these Proceedings for their cooperation with the Board in respect of time limitation, accurate and patient fulfilment of all tiresome requirements, set by the Board. The talks in the Proceedings are arranged in sections in accordance with their presentation at the Seminar.

## Quantum Field Theory and Gravity

Conceptual and Mathematical Advances in the Search for a Unified Framework

Author: Felix Finster,Olaf Müller,Marc Nardmann,Jürgen Tolksdorf,Eberhard Zeidler

Publisher: Springer Science & Business Media

ISBN: 3034800436

Category: Mathematics

Page: 382

View: 4869

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.

## Classical Topology and Quantum States

Author: A. P. Balachandran

Publisher: World Scientific

ISBN: 9789810203290

Category: Mathematics

Page: 358

View: 5134

This book is an introduction to the role of topology in the quantization of classical systems. It is also an introduction to topological solitons with special emphasis on Skyrmions. As regards the first aspect, several issues of current interest are dealt with at a reasonably elementary level. Examples are principal fibre bundles and their role in quantum physics, the possibility of spinorial quantum states in a Lagrangian theory based on tensorial variables, and multiply connected configuration spaces and associated quantum phenomena like the QCD q angle and exotic statistics. The ideas are also illustrated by simple examples such as the spinning particle, the charge-monopole system and strings in 3+1 dimensions. The application of these ideas to quantum gravity is another subject treated at an introductory level. An attempt has been made in this book to introduce the reader to the significance of topology for many distinct physical systems such as spinning particles, the charge- monopole system, strings, Skyrmions, QCD and gravity. The book is an outgrowth of lectures given by the authors at various institutions and conferences.

## Quantum Geometry

A Statistical Field Theory Approach

Author: Jan Ambjørn,Bergfinnur Durhuus

Publisher: Cambridge University Press

ISBN: 9780521461672

Category: Science

Page: 363

View: 5954

Describes random geometry and applications to strings, quantum gravity, topological field theory and membrane physics.

## A new Theory of Gravitation and its Quantization - Version 1.1

Author: Hartwig Poth

Publisher: epubli

ISBN: 3844246541

Category: Science

Page: 48

View: 8152

Lorentz scalar theory of gravitation.

## Quantum Theory of Gravity

Essays in Honor of the Sixtieth Birthday of Bryce S. De Witt

Author: Steven Mark Christensen,Bryce S.: Festschrift DeWitt

ISBN: N.A

Category: Science

Page: 483

View: 3237

The 33 essays in this volume together provide a valuable overview of the progress towards a theory of quantum gravity, and offer succinct treatment of: quantum field theory in curved space-times, supergravity, cosmology, black holes, quantum geometry, supersymmetry and related phenomena.

## Towards Quantum Gravity

Proceedings of the XXXV International Winter School on Theoretical Physics Held in Polanica, Poland, 2–11 February 1999

Author: Jerzy Kowalski-Glikman

Publisher: Springer

ISBN: 3540466347

Category: Science

Page: 376

View: 1090

The aim of this book is to give graduate students an overview of quantum gravity but it also covers related topics from astrophysics. Some well-written contributions can serve as an introduction into basic conceptual concepts like time in quantum gravity or the emergence of a classical world from quantum cosmology. This makes the volume attractive to philosophers of science, too. Other topics are black holes, gravitational waves and non-commutative extensions of physical theories.