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Variational Approach To Gravity Field Theories
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Book Synopsis Variational Approach to Gravity Field Theories by : Alberto Vecchiato
Download or read book Variational Approach to Gravity Field Theories written by Alberto Vecchiato and published by Springer. This book was released on 2017-05-30 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a detailed and stimulating account of the Lagrangian, or variational, approach to general relativity and beyond. The approach more usually adopted when describing general relativity is to introduce the required concepts of differential geometry and derive the field and geodesic equations from purely geometrical properties. Demonstration of the physical meaning then requires the weak field approximation of these equations to recover their Newtonian counterparts. The potential downside of this approach is that it tends to suit the mathematical mind and requires the physicist to study and work in a completely unfamiliar environment. In contrast, the approach to general relativity described in this book will be especially suited to physics students. After an introduction to field theories and the variational approach, individual sections focus on the variational approach in relation to special relativity, general relativity, and alternative theories of gravity. Throughout the text, solved exercises and examples are presented. The book will meet the needs of both students specializing in theoretical physics and those seeking a better understanding of particular aspects of the subject.
Book Synopsis Global Gravity Field Modeling from Satellite-to-Satellite Tracking Data by : Majid Naeimi
Download or read book Global Gravity Field Modeling from Satellite-to-Satellite Tracking Data written by Majid Naeimi and published by Springer. This book was released on 2017-02-10 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a sound theoretical basis for the the different gravity field recovery methods and the numerics of satellite-to-satellite tracking data. It represents lectures given at the ‘Wilhelm and Else Heraeus Autumn School’ in Bad Honnef, Germany, October 4-9, 2015. The emphasis of the school was on providing a sound theoretical basis for the different gravity field recovery methods and the numerics of data analysis. The approaches covered here are the variational equations (classical approach), the acceleration approach and the energy balance approach, all of which are used for global gravity field recovery on the basis of satellite observations. The theory of parameter estimation in satellite gravimetry and concepts for orbit determination are also included. The book guides readers through a broad range of topics in satellite gravimetry, supplemented by the necessary theoretical background and numerical examples. While it provides a comprehensive overview for those readers who are already familiar with satellite gravity data processing, it also offers an essential reference guide for graduate and undergraduate students interested in this field.
Book Synopsis Particles And Quantum Fields by : Hagen Kleinert
Download or read book Particles And Quantum Fields written by Hagen Kleinert and published by World Scientific. This book was released on 2016-05-30 with total page 1628 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introductory book on elementary particles and their interactions. It starts out with many-body Schrödinger theory and second quantization and leads, via its generalization, to relativistic fields of various spins and to gravity. The text begins with the best known quantum field theory so far, the quantum electrodynamics of photon and electrons (QED). It continues by developing the theory of strong interactions between the elementary constituents of matter (quarks). This is possible due to the property called asymptotic freedom. On the way one has to tackle the problem of removing various infinities by renormalization. The divergent sums of infinitely many diagrams are performed with the renormalization group or by variational perturbation theory (VPT). The latter is an outcome of the Feynman-Kleinert variational approach to path integrals discussed in two earlier books of the author, one representing a comprehensive treatise on path integrals, the other dealing with critial phenomena. Unlike ordinary perturbation theory, VPT produces uniformly convergent series which are valid from weak to strong couplings, where they describe critical phenomena.The present book develops the theory of effective actions which allow to treat quantum phenomena with classical formalism. For example, it derives the observed anomalous power laws of strongly interacting theories from an extremum of the action. Their fluctuations are not based on Gaussian distributions, as in the perturbative treatment of quantum field theories, or in asymptotically-free theories, but on deviations from the average which are much larger and which obey power-like distributions.Exactly solvable models are discussed and their physical properties are compared with those derived from general methods. In the last chapter we discuss the problem of quantizing the classical theory of gravity.
Book Synopsis Gravitational Theory, from General Relativity to Unified Field Theories by : Jerry G. Bails
Download or read book Gravitational Theory, from General Relativity to Unified Field Theories written by Jerry G. Bails and published by . This book was released on 1957 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this paper is to consider the General Theory of Relativity. Einstein's gravitational equations are solved for the static field of a single gravitating center. The equations of motion of a particle in this field are then derived. Throughout the discussion it is emphasized that the Newtonian theory remains as a limiting case of the General Theory. Further, the deflection of a ray of light just grazing the sun's limb is shown to be a conclusion of this theory, which Einstein published in 1916 in his famous memoir, "Die Grundlage der allgmeinen Relativitätstheorie". In order to reat the General Theory, it has been necessary first to develop the fundamentals of the tensor calculus. Then the equations for the geodesics are derived and simplified by introducing the Christoffel three-index symbols, whose properties are examined. The fundamental metric tensor and the Riemann-Christoffel tensor are discussed in some detail. These tensors, which measure respectively the metric properties and the Rienmannian curvature, play important roles in the natural geometry developed by Einstein. It has been found entirely satisfactory to introduce the concept of the tensor systematically from the point of view of the definite line integral. Tensor equations are characterized by the fact that they are invariant under coordinate transformations. The fundamental postulate of General Relativity requires that the laws of physics be expressed by equations which hold independently of the coordinate system selected to describe events in Minkowski space. Hence, tensors are indispensable in the formulation of such laws of physics as the law of inertia and the law of gravitation. Just as the Special Theory is clearly limited by its failure to include gravitational phenomena, the General Theory is limited by its failure to embrace Maxwell's equations. This paper discusses three attempts to develop unified field theories that would relate gravitational and electromagnetic penomena in one geometry. Weyl's early attempt to remove a hidden assumption in Riemannian geometry, and introduce the notion of gauge-invariance is sketched for the reader. Einstein's final success in developing unified field equations from a variational principle is discussed briefly, and the present research of Fantappie and Arcidiacono into a Final Relativity is outlined. These two Italian mathematicians have approached the problem of a unified theory from a consideration of the generalization of the Lorentz thransformations of Special Relativity. Their efforts provide one of the most recent approaches to the present problem.
Download or read book Gravitation written by Charles W. Misner and published by Macmillan. This book was released on 1973-09-15 with total page 1324 pages. Available in PDF, EPUB and Kindle. Book excerpt: An in-depth study of Einstein's theory of gravity using modern formalism and notation of differential geometry, and documenting the revolutionary techniques developed to test the theory of general relativity.
Book Synopsis Probabilistic Models of Cosmic Backgrounds by : Anatoliy Malyarenko
Download or read book Probabilistic Models of Cosmic Backgrounds written by Anatoliy Malyarenko and published by CRC Press. This book was released on 2024-06-30 with total page 705 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combining research methods from various areas of mathematics and physics, Probabilistic Models of Cosmic Backgrounds describes the isotropic random sections of certain fibre bundles and their applications to creating rigorous mathematical models of both discovered and hypothetical cosmic backgrounds. Previously scattered and hard-to-find mathematical and physical theories have been assembled from numerous textbooks, monographs, and research papers, and explained from different or even unexpected points of view. This consists of both classical and newly discovered results necessary for understanding a sophisticated problem of modelling cosmic backgrounds. The book contains a comprehensive description of mathematical and physical aspects of cosmic backgrounds with a clear focus on examples and explicit calculations. Its reader will bridge the gap of misunderstanding between the specialists in various theoretical and applied areas who speak different scientific languages. The audience of the book consists of scholars, students, and professional researchers. A scholar will find basic material for starting their own research. A student will use the book as supplementary material for various courses and modules. A professional mathematician will find a description of several physical phenomena at the rigorous mathematical level. A professional physicist will discover mathematical foundations for well-known physical theories.
Book Synopsis Classical Field Theory and the Stress-Energy Tensor by : Mark S. Swanson
Download or read book Classical Field Theory and the Stress-Energy Tensor written by Mark S. Swanson and published by Morgan & Claypool Publishers. This book was released on 2015-10-12 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a concise introduction to the key concepts of classical field theory for beginning graduate students and advanced undergraduate students who wish to study the unifying structures and physical insights provided by classical field theory without dealing with the additional complication of quantization. In that regard, there are many important aspects of field theory that can be understood without quantizing the fields. These include the action formulation, Galilean and relativistic invariance, traveling and standing waves, spin angular momentum, gauge invariance, subsidiary conditions, fluctuations, spinor and vector fields, conservation laws and symmetries, and the Higgs mechanism, all of which are often treated briefly in a course on quantum field theory.
Book Synopsis Gravity, Gauge Theories and Quantum Cosmology by : J.V. Narlikar
Download or read book Gravity, Gauge Theories and Quantum Cosmology written by J.V. Narlikar and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: For several decades since its inception, Einstein's general theory of relativity stood somewhat aloof from the rest of physics. Paradoxically, the attributes which normally boost a physical theory - namely, its perfection as a theoreti cal framework and the extraordinary intellectual achievement underlying i- prevented the general theory from being assimilated in the mainstream of physics. It was as if theoreticians hesitated to tamper with something that is manifestly so beautiful. Happily, two developments in the 1970s have narrowed the gap. In 1974 Stephen Hawking arrived at the remarkable result that black holes radiate after all. And in the second half of the decade, particle physicists discovered that the only scenario for applying their grand unified theories was offered by the very early phase in the history of the Big Bang universe. In both cases, it was necessary to discuss the ideas of quantum field theory in the background of curved spacetime that is basic to general relativity. This is, however, only half the total story. If gravity is to be brought into the general fold of theoretical physics we have to know how to quantize it. To date this has proved a formidable task although most physicists would agree that, as in the case of grand unified theories, quantum gravity will have applications to cosmology, in the very early stages of the Big Bang universe. In fact, the present picture of the Big Bang universe necessarily forces us to think of quantum cosmology.
Download or read book Energy Research Abstracts written by and published by . This book was released on 1991 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Beyond Einstein Gravity by : Salvatore Capozziello
Download or read book Beyond Einstein Gravity written by Salvatore Capozziello and published by Springer. This book was released on 2010-11-30 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Beyond Einstein’s Gravity is a graduate level introduction to extended theories of gravity and cosmology, including variational principles, the weak-field limit, gravitational waves, mathematical tools, exact solutions, as well as cosmological and astrophysical applications. The book provides a critical overview of the research in this area and unifies the existing literature using a consistent notation. Although the results apply in principle to all alternative gravities, a special emphasis is on scalar-tensor and f(R) theories. They were studied by theoretical physicists from early on, and in the 1980s they appeared in attempts to renormalize General Relativity and in models of the early universe. Recently, these theories have seen a new lease of life, in both their metric and metric-affine versions, as models of the present acceleration of the universe without introducing the mysterious and exotic dark energy. The dark matter problem can also be addressed in extended gravity. These applications are contributing to a deeper understanding of the gravitational interaction from both the theoretical and the experimental point of view. An extensive bibliography guides the reader into more detailed literature on particular topics.
Book Synopsis Quantum Statistical Field Theory by : Norman J. M. Horing
Download or read book Quantum Statistical Field Theory written by Norman J. M. Horing and published by Oxford University Press. This book was released on 2017 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: The methods of coupled quantum field theory, which have played a major role in the extensive development of nonrelativistic quantum many-particle theory and condensed matter physics, are at the core of this book.
Book Synopsis The Large N Expansion in Quantum Field Theory and Statistical Physics by : E. Brzin
Download or read book The Large N Expansion in Quantum Field Theory and Statistical Physics written by E. Brzin and published by World Scientific. This book was released on 1993 with total page 1154 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains an edited comprehensive collection of reprints on the subject of the large N limit as applied to a wide spectrum of problems in quantum field theory and statistical mechanics. The topics include (1) Spin Systems; (2) Large N Limit of Gauge Theories; (3) Two-Dimensional QCD; (4) Exact Results on Planar Perturbation Series and the Nature of the 1/N Series; (5) Schwinger-Dyson Equations Approach; (6) QCD Phenomenological Lagrangians and the Large N Limit; (7) Other Approaches to Large N: Eguchi-Kawai Model, Collective Fields and Numerical Methods; (8) Matrix Models; (9) Two-Dimensional Gravity and String Theory.
Book Synopsis Gravity, Particles And Space-time by : P I Pronin
Download or read book Gravity, Particles And Space-time written by P I Pronin and published by World Scientific. This book was released on 1996-04-12 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises original and review articles on the frontier problems of the gravitation theory, theoretical and mathematical physics. The volume is dedicated to the memory of Professor Dmitri Ivanenko who made the great contribution to the physical science of the twentieth century.
Download or read book Nuclear Science Abstracts written by and published by . This book was released on 1976 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Quest For Symmetry, A: Selected Works Of Bunji Sakita by : Keiji Kikkawa
Download or read book Quest For Symmetry, A: Selected Works Of Bunji Sakita written by Keiji Kikkawa and published by World Scientific. This book was released on 1999-04-29 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This important book contains selected research papers of Prof Bunji Sakita. Included are his pioneering papers on SU(6) symmetry, strong coupling theory, string theory, supersymmetry and the method of collective coordinates. There is also a vivid personal account of his journey in physics. The book brings to light some of the key concepts of modern high energy physics.
Book Synopsis Superstrings: The First 15 Years Of Superstring Theory (Reprints + Commentary - In 2 Volumes) by : John H Schwarz
Download or read book Superstrings: The First 15 Years Of Superstring Theory (Reprints + Commentary - In 2 Volumes) written by John H Schwarz and published by World Scientific. This book was released on 1985-09-01 with total page 1168 pages. Available in PDF, EPUB and Kindle. Book excerpt: The discovery by Green and Schwarz in 1984 that ten-dimensional superstring theory is anomaly-free and finite only if the Yang-Mills gauge group is SO(32) or E8 x E8 has made the phenomenological possibilities of superstrings evident. Ths has resulted in a sudden surge of interest in superstrings unification. Since this fast-developing field is new to almost all theoretical physicist, this collection of basic pre-1985 references should be very valuable. This two volumes contain over 1000 pages of reprints plus some introductory comments by J Schwarz.
Book Synopsis Gribov-85 Memorial Volume: Exploring Quantum Field Theory - Proceedings Of The Memorial Workshop Devoted To The 85th Birthday Of V N Gribov by : Yuri L Dokshitzer
Download or read book Gribov-85 Memorial Volume: Exploring Quantum Field Theory - Proceedings Of The Memorial Workshop Devoted To The 85th Birthday Of V N Gribov written by Yuri L Dokshitzer and published by World Scientific. This book was released on 2016-09-16 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vladimir Naumovich Gribov is one of the creators of modern theoretical physics. The concepts and methods that Gribov has developed in the second half of the 20th century became cornerstones of the physics of high energy hadron interactions (relativistic theory of complex angular momenta, a notion of the vacuum pole — Pomeron, effective reggeon field theory), condensed matter physics (critical phenomena), neutrino oscillations, and nuclear physics.His unmatched insights into the nature of the quantum field theory helped to elucidate, in particular, the origin of classical solutions (instantons), quantum anomalies, specific problems in quantization of non-Abelian fields (Gribov anomalies, Gribov horizon), and the role of light quarks in the color confinement phenomenon.The fifth memorial workshop which marked Gribov's 85th birthday took place at the Landau Institute for Theoretical Physics, Russia, in June 2015. Participants of the workshop who came to Chernogolovka from different parts of the world presented new results of studies of many challenging theoretical physics problems across a broad variety of topics, and shared memories about their colleague, great teacher and friend.This book is a collection of the presented talks and contributed papers, which affirm the everlasting impact of Gribov's scientific heritage upon the physics of the 21st century.
