# Search Results for "spacetime-geometry-and-gravitation-progress-in-mathematical-physics"

## Spacetime, Geometry and Gravitation

**Author**: Pankaj Sharan**Publisher:**Springer Science & Business Media**ISBN:**3764399708**Category:**Mathematics**Page:**355**View:**4132

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.

## 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:**2131

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.

## 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:**6184

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.

## 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:**6097

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.

## Gesundheitswissenschaften und öffentliche Gesundheitsförderung

*Aktuelle Modelle für eine Public-health-Ausbildung in der Bundesrepublik Deutschland*

**Author**: Ulrich Laaser,P. Wolters,F.X. Kaufmann**Publisher:**Springer-Verlag**ISBN:**3642750915**Category:**Medical**Page:**249**View:**4593

## Advances in Theoretical and Mathematical Physics

*ATMP.*

**Author**: N.A**Publisher:**N.A**ISBN:**N.A**Category:**Mathematical physics**Page:**N.A**View:**7961

## Further Advances in Twistor Theory

*Curved Twistor Spaces*

**Author**: L.J. Mason,P.Z. Kobak,L. Hughston,K. Pulverer**Publisher:**CRC Press**ISBN:**9781584880479**Category:**Mathematics**Page:**432**View:**781

Although twistor theory originated as an approach to the unification of quantum theory and general relativity, twistor correspondences and their generalizations have provided powerful mathematical tools for studying problems in differential geometry, nonlinear equations, and representation theory. At the same time, the theory continues to offer promising new insights into the nature of quantum theory and gravitation. Further Advances in Twistor Theory, Volume III: Curved Twistor Spaces is actually the fourth in a series of books compiling articles from Twistor Newsletter-a somewhat informal journal published periodically by the Oxford research group of Roger Penrose. Motivated both by questions in differential geometry and by the quest to find a twistor correspondence for general Ricci-flat space times, this volume explores deformed twistor spaces and their applications. Articles from the world's leading researchers in this field-including Roger Penrose-have been written in an informal, easy-to-read style and arranged in four chapters, each supplemented by a detailed introduction. Collectively, they trace the development of the twistor programme over the last 20 years and provide an overview of its recent advances and current status.

## Progress in String, Field and Particle Theory

**Author**: L. Baulieu,Eliezer Rabinovici,Jeff Harvey,Boris Pioline,Paul Windey**Publisher:**Springer Science & Business Media**ISBN:**9401002118**Category:**Science**Page:**509**View:**4131

The NATO Advanced Study Institute and EC Summer School "Progress in String Field and Particle Theory" was held in Cargse from June 25th till July 11th 2002. The main focus of the school was the recent progress in the very ac tive areas of superstring theory, quantum gravity and the theory of elementary particles. It covered topical problems in domains such as duality between gravity and gaugeinteractions, string field theory, tachyon condensation, non-commutative field theory, string cosmology and string phenomenology. The School featured daily introductory lectures and topical seminars. An informal Gong Show session allowed young post-doctoral researchers and senior graduate students to make a concise presentation oftheir current work. The School gave an excellent opportunity to the youngest researchers to establish a close relationship with their seniors and with the lecturers. These proceedings will further serve in fixing the acquired knowledge, and hopefully, become a useful reference for anyone working in this fascinating do main of physics. Some of the contributions provide an elementary introduction to their subject, while other ones are more geared to the specialist. We are deeply indebted to the NATO Division for Scientific Affairs for funding, and for their constant attention for our meetings, and to the European Commission for a High-Level Scientific Conference grant HPCFCT 2001-00298.

## 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:**6867

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.

## Mathematische Werke / Mathematical Works

**Author**: Erich Kähler**Publisher:**Walter de Gruyter**ISBN:**3110905434**Category:**Mathematics**Page:**980**View:**3897

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.

## 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:**7319

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.

## 100 Years of Gravity and Accelerated Frames

*The Deepest Insights of Einstein and Yang-Mills*

**Author**: Jong-Ping Hsu,Dana Fine**Publisher:**World Scientific**ISBN:**9812703403**Category:**Einstein field equations**Page:**623**View:**5448

This collection of papers presents ideas and problems arising over the past 100 years regarding classical and quantum gravity, gauge theories of gravity, and spacetime transformations of accelerated frames. Both Einstein''s theory of gravity and the YangOCoMills theory are gauge invariant. The invariance principles in physics have transcended both kinetic and dynamic properties and are at the very heart of our understanding of the physical world. In this spirit, this book attempts to survey the development of various formulations for gravitational and YangOCoMills fields and spacetime transformations of accelerated frames, and to reveal their associated problems and limitations. The aim is to present some of the leading ideas and problems discussed by physicists and mathematicians. We highlight three aspects: formulations of gravity as a YangOCoMills field, first discussed by Utiyama; problems of gravitational theory, discussed by Feynman, Dyson and others; spacetime properties and the physics of fields and particles in accelerated frames of reference. These unfulfilled aspects of Einstein and YangOCoMills'' profound thoughts present a great challenge to physicists and mathematicians in the 21st century."

## 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:**1412

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 Algebras

*Applications to Mathematics, Physics, and Engineering*

**Author**: Rafal Ablamowicz**Publisher:**Springer Science & Business Media**ISBN:**1461220440**Category:**Mathematics**Page:**626**View:**7520

The invited papers in this volume provide a detailed examination of Clifford algebras and their significance to analysis, geometry, mathematical structures, physics, and applications in engineering. While the papers collected in this volume require that the reader possess a solid knowledge of appropriate background material, they lead to the most current research topics. With its wide range of topics, well-established contributors, and excellent references and index, this book will appeal to graduate students and researchers.

## Gravity, Black Holes, and the Very Early Universe

*An Introduction to General Relativity and Cosmology*

**Author**: Tai L. Chow**Publisher:**Springer Science & Business Media**ISBN:**038773631X**Category:**Science**Page:**280**View:**7670

Here it is, in a nutshell: the history of one genius’s most crucial work – discoveries that were to change the face of modern physics. In the early 1900s, Albert Einstein formulated two theories that would forever change the landscape of physics: the Special Theory of Relativity and the General Theory of Relativity. Respected American academic Professor Tai Chow tells us the story of these discoveries. He details the basic ideas of Einstein, including his law of gravitation. Deftly employing his inimitable writing style, he goes on to explain the physics behind black holes, weaving into his account an explanation of the structure of the universe and the science of cosmology.

## 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:**2036

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.

## A Collection of Polish Works on Philosophical Problems of Time and Spacetime

**Author**: Helena Eilstein**Publisher:**Springer Science & Business Media**ISBN:**9781402006708**Category:**Juvenile Nonfiction**Page:**148**View:**4463

These works concern fundamental philosophical problems of time and spacetime, such as the implications of the absolute and relations concepts of motion for the disputes about the character of spacetime, the role of relativity, quantum mechanics, quantum gravity and noncommutative geometry with respect to the controversy concerning the objectivity of the flow of time, the existence of the future, the concept of branching spacetime. One paper presents the views on time of an outstanding representative of phenomenology, Roman Ingarden, thus enriching the book with some questions of philosophical anthropology and ethics. The collection is mainly addressed to research workers and graduate students.

## 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:**7876

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.

## Foundations of Mathematics and Physics One Century After Hilbert

*New Perspectives*

**Author**: Joseph Kouneiher**Publisher:**Springer**ISBN:**3319648136**Category:**Science**Page:**441**View:**8054

This book explores the rich and deep interplay between mathematics and physics one century after David Hilbert’s works from 1891 to 1933, published by Springer in six volumes. The most prominent scientists in various domains of these disciplines contribute to this volume providing insight to their works, and analyzing the impact of the breakthrough and the perspectives of their own contributions. The result is a broad journey through the most recent developments in mathematical physics, such as string theory, quantum gravity, noncommutative geometry, twistor theory, Gauge and Quantum fields theories, just to mention a few. The reader, accompanied on this journey by some of the fathers of these theories, explores some far reaching interfaces where mathematics and theoretical physics interact profoundly and gets a broad and deep understanding of subjects which are at the core of recent developments in mathematical physics. The journey is not confined to the present state of the art, but sheds light on future developments of the field, highlighting a list of open problems. Graduate students and researchers working in physics, mathematics and mathematical physics will find this journey extremely fascinating. All those who want to benefit from a comprehensive description of all the latest advances in mathematics and mathematical physics, will find this book very useful too.

## Mathematics and Physics

**Author**: MANIN**Publisher:**Birkhäuser**ISBN:**1489967826**Category:**Juvenile Nonfiction**Page:**99**View:**3199