Spacetime, Geometry and Gravitation

Author: Pankaj Sharan

Publisher: Springer Science & Business Media

ISBN: 3764399708

Category: Mathematics

Page: 355

View: 6844

This introductory textbook on the general theory of relativity presents a solid foundation for those who want to learn about relativity. The subject is presented in a physically intuitive, but mathematically rigorous style. The topic of relativity is covered in a broad and deep manner. Besides, the aim is that after reading the book a student should not feel discouraged when she opens advanced texts on general relativity for further reading. The book consists of three parts: An introduction to the general theory of relativity. Geometrical mathematical background material. Topics that include the action principle, weak gravitational fields and gravitational waves, Schwarzschild and Kerr solution, and the Friedman equation in cosmology. The book is suitable for advanced graduates and graduates, but also for established researchers wishing to be educated about the field.

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: 5144

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.

Covariance and Gauge Invariance in Continuum Physics

Application to Mechanics, Gravitation, and Electromagnetism

Author: Lalaonirina R. Rakotomanana

Publisher: Springer

ISBN: 331991782X

Category: Science

Page: 325

View: 3976

This book presents a Lagrangian approach model to formulate various fields of continuum physics, ranging from gradient continuum elasticity to relativistic gravito-electromagnetism. It extends the classical theories based on Riemann geometry to Riemann-Cartan geometry, and then describes non-homogeneous continuum and spacetime with torsion in Einstein-Cartan relativistic gravitation. It investigates two aspects of invariance of the Lagrangian: covariance of formulation following the method of Lovelock and Rund, and gauge invariance where the active diffeomorphism invariance is considered by using local Poincaré gauge theory according to the Utiyama method. Further, it develops various extensions of strain gradient continuum elasticity, relativistic gravitation and electromagnetism when the torsion field of the Riemann-Cartan continuum is not equal to zero. Lastly, it derives heterogeneous wave propagation equations within twisted and curved manifolds and proposes a relation between electromagnetic potential and torsion tensor.

Progress in Mathematical Relativity, Gravitation and Cosmology

Proceedings of the Spanish Relativity Meeting ERE2012, University of Minho, Guimarães, Portugal, September 3-7, 2012

Author: Alfonso García-Parrado,Filipe C. Mena,Filipe Moura,Estelita Vaz

Publisher: Springer Science & Business Media

ISBN: 3642401570

Category: Mathematics

Page: 485

View: 5612

This book contains contributions from the Spanish Relativity Meeting, ERE 2012, held in Guimarães, Portugal, September 2012. It features more than 70 papers on a range of topics in general relativity and gravitation, from mathematical cosmology, numerical relativity and black holes to string theory and quantum gravity. Under the title "Progress in Mathematical Relativity, Gravitation and Cosmology," ERE 2012 was attended by an exceptional international list of over a hundred participants from the five continents and over forty countries. ERE is organized every year by one of the Spanish or Portuguese groups working in this area and is supported by the Spanish Society of Gravitation and Relativity (SEGRE). This book will be of interest to researchers in mathematics and physics.

Advances in Theoretical Physics

Proceedings of the Landau Birthday Symposium, Copenhagen, 13-17 June 1988

Author: Alan H. Luther

Publisher: Elsevier

ISBN: 1483286959

Category: Science

Page: 264

View: 9307

At Copenhagen in June 1988, the 80th Anniversary of the birth of L D Landau, the much respected Soviet physicist and author of the Course on Theoretical Physics, published by Pergamon Press, was celebrated with an International Symposium in his honour. The papers presented at that meeting are published here, providing an overview of recent progress in theoretical physics, covering super-string theories, chaos, high Tc superconductivity and biomolecules.

Space-Time Foliation in Quantum Gravity

Author: Yuki Sato

Publisher: Springer

ISBN: 4431549471

Category: Science

Page: 100

View: 5331

In this thesis, the author considers quantum gravity to investigate the mysterious origin of our universe and its mechanisms. He and his collaborators have greatly improved the analyticity of two models: causal dynamical triangulations (CDT) and n-DBI gravity, with the space-time foliation which is one common factor shared by these two separate models. In the first part, the analytic method of coupling matters to CDT in 2-dimensional toy models is proposed to uncover the underlying mechanisms of the universe and to remove ambiguities remaining in CDT. As a result, the wave function of the 2-dimensional universe where matters are coupled is derived. The behavior of the wave function reveals that the Hausdorff dimension can be changed when the matter is non-unitary. In the second part, the n-DBI gravity model is considered. The author mainly investigates two effects driven by the space-time foliation: the appearance of a new conserved charge in black holes and an extra scalar mode of the graviton. The former implies a breakdown of the black-hole uniqueness theorem while the latter does not show any pathological behavior.

Further Advances in Twistor Theory

Volume II: Integrable Systems, Conformal Geometry and Gravitation

Author: L.J. Mason,L. Hughston

Publisher: CRC Press

ISBN: 9780582004658

Category: Mathematics

Page: 288

View: 4417

Twistor theory is the remarkable mathematical framework that was discovered by Roger Penrose in the course of research into gravitation and quantum theory. It have since developed into a broad, many-faceted programme that attempts to resolve basic problems in physics by encoding the structure of physical fields and indeed space-time itself into the complex analytic geometry of twistor space. Twistor theory has important applications in diverse areas of mathematics and mathematical physics. These include powerful techniques for the solution of nonlinear equations, in particular the self-duality equations both for the Yang-Mills and the Einstein equations, new approaches to the representation theory of Lie groups, and the quasi-local definition of mass in general relativity, to name but a few. This volume and its companions comprise an abundance of new material, including an extensive collection of Twistor Newsletter articles written over a period of 15 years. These trace the development of the twistor programme and its applications over that period and offer an overview on the current status of various aspects of that programme. The articles have been written in an informal and easy-to-read style and have been arranged by the editors into chapter supplemented by detailed introductions, making each volume self-contained and accessible to graduate students and nonspecialists from other fields. Volume II explores applications of flat twistor space to nonlinear problems. It contains articles on integrable or soluble nonlinear equations, conformal differential geometry, various aspects of general relativity, and the development of Penrose's quasi-local mass construction.

Singularity Theory and Gravitational Lensing

Author: Arlie O. Petters,Harold Levine,Joachim Wambsganss

Publisher: Springer Science & Business Media

ISBN: 9780817636685

Category: Mathematics

Page: 603

View: 1914

This monograph is the first to develop a mathematical theory of gravitational lensing. The theory applies to any finite number of deflector planes and highlights the distinctions between single and multiple plane lensing. Introductory material in Parts I and II present historical highlights and the astrophysical aspects of the subject. Part III employs the ideas and results of singularity theory to put gravitational lensing on a rigorous mathematical foundation.

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: 2250

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.

Mathematical Physics 2000

Author: A Fokas,A Grigoryan,T Kibble,B Zegarlinski

Publisher: World Scientific

ISBN: 1783261714

Category: Science

Page: 336

View: 4134

Mathematical physics has made enormous strides over the past few decades, with the emergence of many new disciplines and with revolutionary advances in old disciplines. One of the especially interesting features is the link between developments in mathematical physics and in pure mathematics. Many of the exciting advances in mathematics owe their origin to mathematical physics — superstring theory, for example, has led to remarkable progress in geometry — while very pure mathematics, such as number theory, has found unexpected applications. The beginning of a new millennium is an appropriate time to survey the present state of the field and look forward to likely advances in the future. In this book, leading experts give personal views on their subjects and on the wider field of mathematical physics. The topics covered range widely over the whole field, from quantum field theory to turbulence, from the classical three-body problem to non-equilibrium statistical mechanics. Contents: Modern Mathematical Physics: What It Should Be (L D Faddeev)New Applications of the Chiral Anomaly (J Fröhlich & B Pedrini)Fluctuations and Entropy Driven Space–Time Intermittency in Navier–Stokes Fluids (G Gallavotti)Superstrings and the Unification of the Physical Forces (M B Green)Questions in Quantum Physics: A Personal View (R Haag)What Good are Quantum Field Theory Infinities? (R Jackiw)Constructive Quantum Field Theory (A Jaffe)Fourier's Law: A Challenge to Theorists (F Bonetto et al.)The “Corpuscular” Structure of the Spectra of Operators Describing Large Systems (R A Minlos)Vortex- and Magneto-Dynamics — A Topological Perspective (H K Moffatt)Gauge Theory: The Gentle Revolution (L O'Raifeartaigh)Random Matrices as Paradigm (L Pastur)Wavefunction Collapse as a Real Gravitational Effect (R Penrose)Schrödinger Operators in the Twenty-First Century (B Simon)The Classical Three-Body Problem — Where is Abstract Mathematics, Physical Intuition, Computational Physics Most Powerful? (H A Posch & W Thirring)Infinite Particle Systems and Their Scaling Limits (S R S Varadhan)Supersymmetry: A Personal View (B Zumino) Readership: Mathematicians and physicists. Keywords:London (GB);Proceedings;Congress;Mathematical Physics

Mathematische Werke / Mathematical Works

Author: Erich Kähler

Publisher: Walter de Gruyter

ISBN: 3110905434

Category: Mathematics

Page: 980

View: 2679

Für die meisten Mathematiker und für viele mathematische Physiker ist der Name Erich Kähler eng verbunden mit wichtigen Begriffen der Geometrie wie zum Beispiel Kähler-Metrik, Kähler-Mannigfaltigkeiten und Kähler-Gruppen. Diese Begriffe gehen alle auf ein 14-seitiges Papier aus dem Jahr 1932 zurück. Dabei handelt es sich jedoch nur um einen sehr kleinen Teil der vielen herausragenden Leistungen Kählers, die ein ungewöhnlich breites Spektrum umfassen: Von der Himmelsmechanik gelangte er zur komplexen Funktionentheorie, zu Differenzialgleichungen, zu analytischer und komplexer Geometrie mit Differenzialformen und schließlich zu seinem eigentlichen Hauptthema, der arithmetischen Geometrie, in der er ein Begriffssystem schuf, das der Vorläufer des heute verwendeten Systems von Grothendieck und Dieudonné ist und in weiten Teilen mit diesem übereinstimmt. Sein Hauptinteresse war es, die Gemeinsamkeiten in der Vielfalt der mathematischen Themen zu finden und so Mathematik als universelle Sprache zu etablieren.

Advances in String Theory

The First Sowers Workshop in Theoretical Physics

Author: Eric R. Sharpe,Arthur Greenspoon

Publisher: American Mathematical Soc.

ISBN: 0821847643

Category: Mathematics

Page: 244

View: 9479

Over the past decade string theory has had an increasing impact on many areas of physics: high energy and hadronic physics, gravitation and cosmology, mathematical physics and even condensed matter physics. The impact has been through many major conceptual and methodological developments in quantum field theory in the past fifteen years. In addition, string theory has exerted a dramatic influence on developments in contemporary mathematics, including Gromov-Witten theory, mirror symmetry in complex and symplectic geometry, and important ramifications in enumerative geometry. This volume is derived from a conference of younger leading practitioners around the common theme: "What is string theory?" The talks covered major current topics, both mathematical and physical, related to string theory. Graduate students and research mathematicians interested in string theory in mathematics and physics will be interested in this workshop.

Advances in theoretical physics

Landau Memorial Conference, Chernogolovka, Russia, 22-26 June 2008

Author: Vladimir Lebedev,Michail Victorovich Feigelman

Publisher: Amer Inst of Physics

ISBN: 9780735406711

Category: Science

Page: 220

View: 4517

The conference "Advances in Theoretical Physics," held in Chernogolovka, Russia, is devoted to Lev Landau's 100 year anniversary. It was organized by the Landau Institute for Theoretical Physics, which was established by Landau's pupils who carried on his traditions. The conference reviews current progress in the main branches of theoretical physics. The talks covered solid state physics and cosmology, low temperature physics and optics, quantum field theory and statistical physics, physics of low-dimensional systems and hydrodynamics.

Quantum Gravity

From Theory to Experimental Search

Author: Domenico J. W. Giulini,Claus Kiefer,Claus Lämmerzahl

Publisher: Springer Science & Business Media

ISBN: 9783540408109

Category: Science

Page: 402

View: 3157

The relation between quantum theory and the theory of gravitation remains one of the most outstanding unresolved issues of modern physics. According to general expectation, general relativity as well as quantum (field) theory in a fixed background spacetime cannot be fundamentally correct. Hence there should exist a broader theory comprising both in appropriate limits, i.e., quantum gravity. This book gives readers a comprehensive introduction accessible to interested non-experts to the main issues surrounding the search for quantum gravity. These issues relate to fundamental questions concerning the various formalisms of quantization; specific questions concerning concrete processes, like gravitational collapse or black-hole evaporation; and the all important question concerning the possibility of experimental tests of quantum-gravity effects.

Clifford (Geometric) Algebras

With Applications in Physics, Mathematics, and Engineering

Author: William E. Baylis

Publisher: Springer Science & Business Media

ISBN: 9780817638689

Category: Mathematics

Page: 517

View: 9505

This volume is an outgrowth of the 1995 Summer School on Theoretical Physics of the Canadian Association of Physicists (CAP), held in Banff, Alberta, in the Canadian Rockies, from July 30 to August 12,1995. The chapters, based on lectures given at the School, are designed to be tutorial in nature, and many include exercises to assist the learning process. Most lecturers gave three or four fifty-minute lectures aimed at relative novices in the field. More emphasis is therefore placed on pedagogy and establishing comprehension than on erudition and superior scholarship. Of course, new and exciting results are presented in applications of Clifford algebras, but in a coherent and user-friendly way to the nonspecialist. The subject area of the volume is Clifford algebra and its applications. Through the geometric language of the Clifford-algebra approach, many concepts in physics are clarified, united, and extended in new and sometimes surprising directions. In particular, the approach eliminates the formal gaps that traditionally separate clas sical, quantum, and relativistic physics. It thereby makes the study of physics more efficient and the research more penetrating, and it suggests resolutions to a major physics problem of the twentieth century, namely how to unite quantum theory and gravity. The term "geometric algebra" was used by Clifford himself, and David Hestenes has suggested its use in order to emphasize its wide applicability, and b& cause the developments by Clifford were themselves based heavily on previous work by Grassmann, Hamilton, Rodrigues, Gauss, and others.

Trends in Mathematical Physics

Proceedings of the Conference on Trends in Mathematical Physics, October 14-17, 1998, University of Tennessee, Knoxville

Author: Vasilios Alexiades,George Siopsis

Publisher: American Mathematical Soc.

ISBN: 0821820060

Category: Science

Page: 527

View: 4284

This volume presents the proceedings of the conference on ``Trends in Mathematical Physics'' held at the University of Tennessee. The conference drew international experts from mathematical and computational physics. The following topics were addressed: superstrings and quantum gravity, pattern formation, and crystallographic topology. The cutting-edge research reflected in the extensive surveys in the book are written for a diverse audience.

Advances in gravitation and cosmology

proceedings of the Second International Conference on Gravitation and Cosmology, Ahmedabad, India, 13-18 December 1991

Author: B. R. Iyer

Publisher: Wiley Eastern Ltd

ISBN: 9788122405224

Category: Science

Page: 287

View: 743