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| modern twistor theory: An Introduction to Twistor Theory S. A. Huggett, K. P. Tod, 1994-07-21 This book is an introduction to twistor theory and modern geometrical approaches to space-time structure at the graduate or advanced undergraduate level. It will be valuable also to the physicist as an introduction to some of the mathematics that has proved useful in these areas, and to the mathematician as an example of where sheaf cohomology and complex manifold theory can be used in physics. |
| modern twistor theory: Twistor Geometry and Field Theory R. S. Ward, Raymond O'Neil Wells (Jr.), 1990 Deals with the twistor treatment of certain linear and non-linear partial differential equations. The description in terms of twistors involves algebraic and differential geometry, and several complex variables. |
| modern twistor theory: Fashion, Faith, and Fantasy in the New Physics of the Universe Roger Penrose, 2024-10-22 Nobel Prize–winning physicist Roger Penrose questions some of the most fashionable ideas in physics today, including string theory What can fashionable ideas, blind faith, or pure fantasy possibly have to do with the scientific quest to understand the universe? Surely, theoretical physicists are immune to mere trends, dogmatic beliefs, or flights of fancy? In fact, acclaimed physicist and bestselling author Roger Penrose argues that researchers working at the extreme frontiers of physics are just as susceptible to these forces as anyone else. In this provocative book, he argues that fashion, faith, and fantasy, while sometimes productive and even essential in physics, may be leading today's researchers astray in three of the field's most important areas—string theory, quantum mechanics, and cosmology. Arguing that string theory has veered away from physical reality by positing six extra hidden dimensions, Penrose cautions that the fashionable nature of a theory can cloud our judgment of its plausibility. In the case of quantum mechanics, its stunning success in explaining the atomic universe has led to an uncritical faith that it must also apply to reasonably massive objects, and Penrose responds by suggesting possible changes in quantum theory. Turning to cosmology, he argues that most of the current fantastical ideas about the origins of the universe cannot be true, but that an even wilder reality may lie behind them. Finally, Penrose describes how fashion, faith, and fantasy have ironically also shaped his own work, from twistor theory, a possible alternative to string theory that is beginning to acquire a fashionable status, to conformal cyclic cosmology, an idea so fantastic that it could be called conformal crazy cosmology. The result is an important critique of some of the most significant developments in physics today from one of its most eminent figures. |
| modern twistor theory: Further Advances in Twistor Theory L.J. Mason, L. Hughston, 1995-04-04 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. |
| modern twistor theory: Not Even Wrong Peter Woit, 2011-08-31 Not Even Wrong is a fascinating exploration of our attempts to come to grips with perhaps the most intellectually demanding puzzle of all: how does the universe work at its most fundamnetal level? The book begins with an historical survey of the experimental and theoretical developments that led to the creation of the phenomenally successful 'Standard Model' of particle physics around 1975. Despite its successes, the Standard Model does not answer all the key questions and physicists continuing search for answers led to the development of superstring theory. However, after twenty years, superstring theory has failed to advance beyond the Standard Model. The absence of experimental evidence is at the core of this controversial situation which means that it is impossible to prove that superstring theory is either right or wrong. To date, only the arguments of the theory's advocates have received much publicity. Not Even Wrong provides readers with another side of the story. |
| modern twistor theory: The Road to Reality Roger Penrose, 2021-06-09 **WINNER OF THE 2020 NOBEL PRIZE IN PHYSICS** The Road to Reality is the most important and ambitious work of science for a generation. It provides nothing less than a comprehensive account of the physical universe and the essentials of its underlying mathematical theory. It assumes no particular specialist knowledge on the part of the reader, so that, for example, the early chapters give us the vital mathematical background to the physical theories explored later in the book. Roger Penrose's purpose is to describe as clearly as possible our present understanding of the universe and to convey a feeling for its deep beauty and philosophical implications, as well as its intricate logical interconnections. The Road to Reality is rarely less than challenging, but the book is leavened by vivid descriptive passages, as well as hundreds of hand-drawn diagrams. In a single work of colossal scope one of the world's greatest scientists has given us a complete and unrivalled guide to the glories of the universe that we all inhabit. 'Roger Penrose is the most important physicist to work in relativity theory except for Einstein. He is one of the very few people I've met in my life who, without reservation, I call a genius' Lee Smolin |
| modern twistor theory: An Introduction to Twistor Theory S. A. Huggett, K. P. Tod, 1994 Evolving from graduate lectures given in London and Oxford, this introduction to twistor theory and modern geometrical approaches to space-time structure will provide graduate students with the basics of twistor theory, presupposing some knowledge of special relativity and differenttial geometry. |
| modern twistor theory: The Complete Idiot's Guide to String Theory George Musser, 2008-07-01 We’re living in the midst of a scientific revolution that’s captured the general public’s attention and imagination. The aim of this new revolution is to develop a “theory of everything”—a set of laws of physics that will explain all that can be explained, ranging from the tiniest subatomic particle to the universe as a whole. Here, readers will learn the ideas behind the theories, and their effects upon our world, our civilization, and ourselves. The Complete Idiot’s Guide® String Theory explains how this exciting idea holds up against competing theories. In this Complete Idiot’s Guide®, you get: • Clear explanation of quantum mechanics, Einstein’s theories of relativity, and how string theory unites them. • A quick, easy-to-understand overview of competing theories and how they might be tested. • Fast facts about black holes, what’s inside them, how they’re made, and why they’re so paradoxical. • Simple, smart tips to help you visualize extra dimensions. |
| modern twistor theory: A Brief History of String Theory Dean Rickles, 2014-02-18 During its forty year lifespan, string theory has always had the power to divide, being called both a 'theory of everything' and a 'theory of nothing'. Critics have even questioned whether it qualifies as a scientific theory at all. This book adopts an objective stance, standing back from the question of the truth or falsity of string theory and instead focusing on how it came to be and how it came to occupy its present position in physics. An unexpectedly rich history is revealed, with deep connections to our most well-established physical theories. Fully self-contained and written in a lively fashion, the book will appeal to a wide variety of readers from novice to specialist. |
| modern twistor theory: The Penrose Transform Robert J. Baston, Michael G. Eastwood, 2016-10-28 Geared toward students of physics and mathematics; presupposes no familiarity with twistor theory. A huge amount of information, well organized and condensed into less than 200 pages. — Mathematical Reviews. 1989 edition. |
| modern twistor theory: Quantum Gravity, Quantum Cosmology and Lorentzian Geometries Giampiero Esposito, 2009-02-13 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. |
| modern twistor theory: Solitons, Instantons, and Twistors Maciej Dunajski, 2010 A text aimed at third year undergraduates and graduates in mathematics and physics, presenting elementary twistor theory as a universal technique for solving differential equations in applied mathematics and theoretical physics. |
| modern twistor theory: The Mathematical Theory of Black Holes Subrahmanyan Chandrasekhar, 1998 The theory of black holes is the most simple consequence of Einstein's relativity theory. Dealing with relativity theory, this book details one of the most beautiful areas of mathematical physics; the theory of black holes. It represents a personal testament to the work of the author, who spent several years working-out the subject matter.--WorldCat. |
| modern twistor theory: The Physics of Quantum Mechanics James Binney, David Skinner, 2013-12 This title gives students a good understanding of how quantum mechanics describes the material world. The text stresses the continuity between the quantum world and the classical world, which is merely an approximation to the quantum world. |
| modern twistor theory: The Strangest Man Graham Farmelo, 2009-01-22 'A monumental achievement - one of the great scientific biographies.' Michael Frayn The Strangest Man is the Costa Biography Award-winning account of Paul Dirac, the famous physicist sometimes called the British Einstein. He was one of the leading pioneers of the greatest revolution in twentieth-century science: quantum mechanics. The youngest theoretician ever to win the Nobel Prize for Physics, he was also pathologically reticent, strangely literal-minded and legendarily unable to communicate or empathize. Through his greatest period of productivity, his postcards home contained only remarks about the weather.Based on a previously undiscovered archive of family papers, Graham Farmelo celebrates Dirac's massive scientific achievement while drawing a compassionate portrait of his life and work. Farmelo shows a man who, while hopelessly socially inept, could manage to love and sustain close friendship.The Strangest Man is an extraordinary and moving human story, as well as a study of one of the most exciting times in scientific history. 'A wonderful book . . . Moving, sometimes comic, sometimes infinitely sad, and goes to the roots of what we mean by truth in science.' Lord Waldegrave, Daily Telegraph |
| modern twistor theory: Warped Passages Lisa Randall, 2006-09-19 The universe has many secrets. It may hide additional dimensions of space other than the familier three we recognize. There might even be another universe adjacent to ours, invisible and unattainable . . . for now. Warped Passages is a brilliantly readable and altogether exhilarating journey that tracks the arc of discovery from early twentieth-century physics to the razor's edge of modern scientific theory. One of the world's leading theoretical physicists, Lisa Randall provides astonishing scientific possibilities that, until recently, were restricted to the realm of science fiction. Unraveling the twisted threads of the most current debates on relativity, quantum mechanics, and gravity, she explores some of the most fundamental questions posed by Nature—taking us into the warped, hidden dimensions underpinning the universe we live in, demystifying the science of the myriad worlds that may exist just beyond our own. |
| modern twistor theory: A Project to Find the Fundamental Theory of Physics Stephen Wolfram, 2020 The Wolfram Physics Project is a bold effort to find the fundamental theory of physics. It combines new ideas with the latest research in physics, mathematics and computation in the push to achieve this ultimate goal of science. Written with Stephen Wolfram's characteristic expository flair, this book provides a unique opportunity to learn about a historic initiative in science right as it is happening. A Project to Find the Fundamental Theory of Physics includes an accessible introduction to the project as well as core technical exposition and rich, never-before-seen visualizations. |
| modern twistor theory: Quantum Theory, Groups and Representations Peter Woit, 2017-11-01 This text systematically presents the basics of quantum mechanics, emphasizing the role of Lie groups, Lie algebras, and their unitary representations. The mathematical structure of the subject is brought to the fore, intentionally avoiding significant overlap with material from standard physics courses in quantum mechanics and quantum field theory. The level of presentation is attractive to mathematics students looking to learn about both quantum mechanics and representation theory, while also appealing to physics students who would like to know more about the mathematics underlying the subject. This text showcases the numerous differences between typical mathematical and physical treatments of the subject. The latter portions of the book focus on central mathematical objects that occur in the Standard Model of particle physics, underlining the deep and intimate connections between mathematics and the physical world. While an elementary physics course of some kind would be helpful to the reader, no specific background in physics is assumed, making this book accessible to students with a grounding in multivariable calculus and linear algebra. Many exercises are provided to develop the reader's understanding of and facility in quantum-theoretical concepts and calculations. |
| modern twistor theory: Further Advances in Twistor Theory L.J. Mason, L.P. Hughston, P.Z. Kobak, 2023-05-31 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 non-specialists 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. |
| modern twistor theory: Quantum Field Theory in a Nutshell Anthony Zee, 2010-02-01 A fully updated edition of the classic text by acclaimed physicist A. Zee Since it was first published, Quantum Field Theory in a Nutshell has quickly established itself as the most accessible and comprehensive introduction to this profound and deeply fascinating area of theoretical physics. Now in this fully revised and expanded edition, A. Zee covers the latest advances while providing a solid conceptual foundation for students to build on, making this the most up-to-date and modern textbook on quantum field theory available. This expanded edition features several additional chapters, as well as an entirely new section describing recent developments in quantum field theory such as gravitational waves, the helicity spinor formalism, on-shell gluon scattering, recursion relations for amplitudes with complex momenta, and the hidden connection between Yang-Mills theory and Einstein gravity. Zee also provides added exercises, explanations, and examples, as well as detailed appendices, solutions to selected exercises, and suggestions for further reading. The most accessible and comprehensive introductory textbook available Features a fully revised, updated, and expanded text Covers the latest exciting advances in the field Includes new exercises Offers a one-of-a-kind resource for students and researchers Leading universities that have adopted this book include: Arizona State University Boston University Brandeis University Brown University California Institute of Technology Carnegie Mellon College of William & Mary Cornell Harvard University Massachusetts Institute of Technology Northwestern University Ohio State University Princeton University Purdue University - Main Campus Rensselaer Polytechnic Institute Rutgers University - New Brunswick Stanford University University of California - Berkeley University of Central Florida University of Chicago University of Michigan University of Montreal University of Notre Dame Vanderbilt University Virginia Tech University |
| modern twistor theory: Three Roads To Quantum Gravity Lee Smolin, 2008-03-18 It would be hard to imagine a better guide to this difficult subject. -- Scientific American In Three Roads to Quantum Gravity, Lee Smolin provides an accessible overview of the attempts to build a final theory of everything. He explains in simple terms what scientists are talking about when they say the world is made from exotic entities such as loops, strings, and black holes and tells the fascinating stories behind these discoveries: the rivalries, epiphanies, and intrigues he witnessed firsthand. Provocative, original, and unsettling. -- The New York Review of Books An excellent writer, a creative thinker. -- Nature |
| modern twistor theory: Twistors in Mathematics and Physics T. N. Bailey, R. J. Baston, 1990-08-23 This 1990 collection of review articles covers the considerable progress made in a wide range of applications of twistor theory. |
| modern twistor theory: A New Kind of Science Stephen Wolfram, 2018-11-30 NOW IN PAPERBACK€Starting from a collection of simple computer experiments€illustrated in the book by striking computer graphics€Stephen Wolfram shows how their unexpected results force a whole new way of looking at the operation of our universe. |
| modern twistor theory: Integrable Systems N.J. Hitchin, G. B. Segal, R.S. Ward, 2013-03-14 Designed to give graduate students an understanding of integrable systems via the study of Riemann surfaces, loop groups, and twistors, this book has its origins in a lecture series given by the internationally renowned authors. Written in an accessible, informal style, it fills a gap in the existing literature. |
| modern twistor theory: Introduction to Strings and Branes Peter West, 2012-07-05 Supersymmetry, strings and branes are believed to be the essential ingredients in a single unified consistent theory of physics. This book gives a detailed, step-by-step introduction to the theoretical foundations required for research in strings and branes. After a study of the different formulations of the bosonic and supersymmetric point particles, the classical and quantum bosonic and supersymmetric string theories are presented. This book includes accounts of brane dynamics and D-branes and the T, S and U duality symmetries of string theory. The historical derivation of string theory is given as well as the sum over the world-sheet approach to the interacting string. More advanced topics include string field theory and Kac–Moody symmetries. The book contains pedagogical accounts of conformal quantum field theory, supergravity theories, Clifford algebras and spinors, and Lie algebras. It is essential reading for graduate students and researchers wanting to learn strings and branes. |
| modern twistor theory: Everything is Now Bill Spence, 2020-10-27 This engaging and beautifully written book gives an authoritative but accessible account of some of the most exciting and unexpected recent developments in theoretical physics. – Professor Lionel J Mason, Mathematical Institute, University of Oxford String theory is often paraded as a theory of everything, but there are a large number of untold stories in which string theory gives us insight into other areas of physics. Here, Bill Spence does an excellent job of explaining the deep connections between string theory, particle physics, and the novel way of viewing space and time. – Professor David Tong, Department of Applied Mathematics and Theoretical Physics, University of Cambridge Foremost amongst Nature’s closest-guarded secrets is how to unite Einstein’s theory of gravity with quantum theory – thereby creating a ‘quantum space-time’. This problem has been unsolved now for more than a century, with the standard methods of physics making little headway. It is clear that much more radical ideas are needed, and our front-line researchers are showing that string theory provides these. This book describes these extraordinary developments, which are helping us to think in entirely new ways about how physical reality may be structured at its deepest level. Amongst these ideas are that Everything can happen at the same time – it is all Now; Hidden spaces, large and small, are everywhere amongst us; The basic objects are ‘membranes’ that behave like soap bubbles and can explore the shape of spacetime in new ways; We are holographic projections from higher dimensions; You can take the ‘square root’ of gravity; Ideas from the ancient Greeks are resurfacing in a beautiful new form; And the very latest work shows that ‘staying positive’ is essential. The book is aimed at a general audience, using analogies, diagrams, and simple examples throughout. It is intended as a brief tour, enabling the reader to become aware of the main ideas and recent work. A full list of further resources is supplied. Bill Spence is the founding Director of the Centre for Research in String Theory at Queen Mary University of London. He has worked on string theory for over three decades. |
| modern twistor theory: Bankrupting Physics Alexander Unzicker, Sheilla Jones, 2013-07-30 An award-winning scientist argues that theoretical physics has become too abstract and calls for science to return to the experimental method The recently celebrated discovery of the Higgs boson has captivated the public's imagination with the promise that it can explain the origins of everything in the universe. It's no wonder that the media refers to it grandly as the God particle. Yet behind closed doors, physicists are admitting that there is much more to this story, and even years of gunning the Large Hadron Collider and herculean number crunching may still not lead to a deep understanding of the laws of nature. In this fascinating and eye-opening account, theoretical physicist Alexander Unzicker and science writer Sheilla Jones offer a polemic. They question whether the large-scale, multinational enterprises actually lead us to the promised land of understanding the universe. The two scientists take us on a tour of contemporary physics and show how a series of highly publicized theories met a dead end. Unzicker and Jones systematically unpack the recent hot theories such as parallel universes, string theory, and inflationary cosmology, and provide an accessible explanation of each. The auhors argue that physics has abandoned its evidence-based roots and shifted to untestable mathematical theories, and they issue a clarion call for the science to return to its experimental foundation. |
| modern twistor theory: Connections In Classical And Quantum Field Theory Luigi Mangiarotti, Gennadi A Sardanashvily, 2000-04-28 Geometrical notions and methods play an important role in both classical and quantum field theory, and a connection is a deep structure which apparently underlies the gauge-theoretical models in field theory and mechanics. This book is an encyclopaedia of modern geometric methods in theoretical physics. It collects together the basic mathematical facts about various types of connections, and provides a detailed exposition of relevant physical applications. It discusses the modern issues concerning the gauge theories of fundamental fields. The authors have tried to give all the necessary mathematical background, thus making the book self-contained.This book should be useful to graduate students, physicists and mathematicians who are interested in the issue of deep interrelations between theoretical physics and geometry. |
| modern twistor theory: Zero to Infinity Peter Rowlands, 2007 Unique in its field, this book uses a methodology that is entirely new, creating the simplest and most abstract foundations for physics to date. The author proposes a fundamental description of process in a universal computational rewrite system, leading to an irreducible form of relativistic quantum mechanics from a single operator. This is not only simpler, and more fundamental, but also seemingly more powerful than any other quantum mechanics formalism available. The methodology finds immediate applications in particle physics, theoretical physics and theoretical computing. In addition, taking the rewrite structure more generally as a description of process, the book shows how it can be applied to large-scale structures beyond the realm of fundamental physics. Sample Chapter(s). Chapter 1: Zero (228 KB). Contents: Zero; Why Does Physics Work?; The Emergence of Physics; Groups and Representations; Breaking the Dirac Code; The Dirac Nilpotent; Nonrelativistic Quantum Mechanics and the Classical Transition; The Classical and Special Relativistic Approximations; The Resolution of Paradoxes; Electric, Strong and Weak Interactions; QED and Its Analogues; Vacuum; Fermion and Boson Structures; A Representation of Strong and Weak Interactions; Grand Unification and Particle Masses; The Factor 2 and Duality; Gravity and Inertia; Dimensionality, Strings and Quantum Gravity; Nature''s Code; Nature''s Rule; Infinity. Readership: Researchers in quantum, theoretical and high energy physics. |
| modern twistor theory: Asymptotically Symmetric Einstein Metrics Olivier Biquard, 2006 The correspondence between Einstein metrics and their conformal boundaries has recently been the focus of great interest. This is particularly so in view of the relation with the physical theory of the AdS/CFT correspondence. In this book, this correspondence is seen in the wider context of asymptotically symmetric Einstein metrics, that is Einstein metrics whose curvature is asymptotic to that of a rank one symmetric space. There is an emphasis on the correspondence between Einstein metrics and geometric structures on their boundary at infinity: conformal structures, CR structures, and quaternionic contact structures introduced and studied in the book. Two new constructions of such Einstein metrics are given, using two different kinds of techniques: analytic methods to construct complete Einstein metrics, with a unified treatment of all rank one symmetric spaces, relying on harmonic analysis; algebraic methods (twistor theory) to construct local solutions of the Einstein equation near the boundary. |
| modern twistor theory: Gauge/Gravity Duality Martin Ammon, Johanna Erdmenger, 2015-04-09 Gauge/gravity duality creates new links between quantum theory and gravity. It has led to new concepts in mathematics and physics, and provides new tools to solve problems in many areas of theoretical physics. This book is the first textbook on this important topic, enabling graduate students and researchers in string theory and particle, nuclear and condensed matter physics to get acquainted with the subject. Focusing on the fundamental aspects as well as on the applications, this textbook guides readers through a thorough explanation of the central concepts of gauge/gravity duality. For the AdS/CFT correspondence, it explains in detail how string theory provides the conjectured map. Generalisations to less symmetric cases of gauge/gravity duality and their applications are then presented, in particular to finite temperature and density, hydrodynamics, QCD-like theories, the quark-gluon plasma and condensed matter systems. The textbook features a large number of exercises, with solutions available online at www.cambridge.org/9781107010345. |
| modern twistor theory: Roger Penrose Roger Penrose, 2011 |
| modern twistor theory: Cartan for Beginners Thomas Andrew Ivey, J. M. Landsberg, 2003 This book is an introduction to Cartan's approach to differential geometry. Two central methods in Cartan's geometry are the theory of exterior differential systems and the method of moving frames. This book presents thorough and modern treatments of both subjects, including their applications to both classic and contemporary problems. It begins with the classical geometry of surfaces and basic Riemannian geometry in the language of moving frames, along with an elementary introduction to exterior differential systems. Key concepts are developed incrementally with motivating examples leading to definitions, theorems, and proofs. Once the basics of the methods are established, the authors develop applications and advanced topics.One notable application is to complex algebraic geometry, where they expand and update important results from projective differential geometry. The book features an introduction to $G$-structures and a treatment of the theory of connections. The Cartan machinery is also applied to obtain explicit solutions of PDEs via Darboux's method, the method of characteristics, and Cartan's method of equivalence. This text is suitable for a one-year graduate course in differential geometry, and parts of it can be used for a one-semester course. It has numerous exercises and examples throughout. It will also be useful to experts in areas such as PDEs and algebraic geometry who want to learn how moving frames and exterior differential systems apply to their fields. |
| modern twistor theory: Quasicrystals and Geometry Marjorie Senechal, 1996-09-26 This first-ever detailed account of quasicrystal geometry will be of great value to mathematicians at all levels with an interest in quasicrystals and geometry, and will also be of interest to graduate students and researchers in solid state physics, crystallography and materials science. |
| modern twistor theory: Spin Geometry H. Blaine Lawson, Marie-Louise Michelsohn, 2016-06-02 This book offers a systematic and comprehensive presentation of the concepts of a spin manifold, spinor fields, Dirac operators, and A-genera, which, over the last two decades, have come to play a significant role in many areas of modern mathematics. Since the deeper applications of these ideas require various general forms of the Atiyah-Singer Index Theorem, the theorems and their proofs, together with all prerequisite material, are examined here in detail. The exposition is richly embroidered with examples and applications to a wide spectrum of problems in differential geometry, topology, and mathematical physics. The authors consistently use Clifford algebras and their representations in this exposition. Clifford multiplication and Dirac operator identities are even used in place of the standard tensor calculus. This unique approach unifies all the standard elliptic operators in geometry and brings fresh insights into curvature calculations. The fundamental relationships of Clifford modules to such topics as the theory of Lie groups, K-theory, KR-theory, and Bott Periodicity also receive careful consideration. A special feature of this book is the development of the theory of Cl-linear elliptic operators and the associated index theorem, which connects certain subtle spin-corbordism invariants to classical questions in geometry and has led to some of the most profound relations known between the curvature and topology of manifolds. |
| modern twistor theory: The Quantum Handshake John G. Cramer, 2015-12-23 This book shines bright light into the dim recesses of quantum theory, where the mysteries of entanglement, nonlocality, and wave collapse have motivated some to conjure up multiple universes, and others to adopt a shut up and calculate mentality. After an extensive and accessible introduction to quantum mechanics and its history, the author turns attention to his transactional model. Using a quantum handshake between normal and time-reversed waves, this model provides a clear visual picture explaining the baffling experimental results that flow daily from the quantum physics laboratories of the world. To demonstrate its powerful simplicity, the transactional model is applied to a collection of counter-intuitive experiments and conceptual problems. |
| modern twistor theory: Integrability, Self-duality, and Twistor Theory Lionel J. Mason, Nicholas Michael John Woodhouse, 1996 It has been known for some time that many of the familiar integrable systems of equations are symmetry reductions of self-duality equations on a metric or on a Yang-Mills connection (for example, the Korteweg-de Vries and nonlinear Schr ̈ odinger equations are reductions of the self-dual Yang-Mills equation). This book explores in detail the connections between self-duality and integrability, and also the application of twistor techniques to integrable systems. It has two central themes: first, that the symmetries of self-duality equations provide a natural classification scheme for integrable systems; and second that twistor theory provides a uniform geometric framework for the study of B ̈ acklund tranformations, the inverse scattering method, and other such general constructions of integrability theory, and that it elucidates the connections between them. |
| modern twistor theory: Introduction to Superanalysis F.A. Berezin, 2013-04-09 TO SUPERANAL YSIS Edited by A.A. KIRILLOV Translated from the Russian by J. Niederle and R. Kotecky English translation edited and revised by Dimitri Leites SPRINGER-SCIENCE+BUSINESS MEDIA, B.V. Library of Congress Cataloging-in-Publication Data Berezin, F.A. (Feliks Aleksandrovich) Introduction to superanalysis. (Mathematical physics and applied mathematics; v. 9) Part I is translation of: Vvedenie v algebru i analiz s antikommutirurushchimi peremennymi. Bibliography: p. Includes index. 1. Mathetical analysis. I. Title. II. Title: Superanalysis. III. Series. QA300. B459 1987 530. 15'5 87-16293 ISBN 978-90-481-8392-0 ISBN 978-94-017-1963-6 (eBook) DOI 10. 1007/978-94-017-1963-6 All Rights Reserved © 1987 by Springer Science+Business Media Dordrecht Originally published by D. Reidel Publishing Company, Dordrecht, Holland in 1987 No part of the material protected by this copyright notice may be reproduced in whole or in part or utilized in any form or by any means electronic or mechanical including photocopying recording or storing in any electronic information system without first obtaining the written permission of the copyright owner. CONTENTS EDITOR'S FOREWORD ix INTRODUCTION 1 1. The Sources 1 2. Supermanifolds 3 3. Additional Structures on Supermanifolds 11 4. Representations of Lie Superalgebras and Supergroups 21 5. Conclusion 23 References 24 PART I CHAPTER 1. GRASSMANN ALGEBRA 29 1. Basic Facts on Associative Algebras 29 2. Grassmann Algebras 35 3. Algebras A(U) 55 CHAPTER 2. SUPERANAL YSIS 74 1. Derivatives 74 2. Integral 76 CHAPTER 3. LINEAR ALGEBRA IN Zz-GRADED SPACES 90 1. |
| modern twistor theory: String Theory For Dummies Andrew Zimmerman Jones, 2009-11-16 A clear, plain-English guide to this complex scientific theory String theory is the hottest topic in physics right now, with books on the subject (pro and con) flying out of the stores. String Theory For Dummies offers an accessible introduction to this highly mathematical theory of everything, which posits ten or more dimensions in an attempt to explain the basic nature of matter and energy. Written for both students and people interested in science, this guide explains concepts, discusses the string theory's hypotheses and predictions, and presents the math in an approachable manner. It features in-depth examples and an easy-to-understand style so that readers can understand this controversial, cutting-edge theory. |
| modern twistor theory: Einstein Gravity in a Nutshell A. Zee, 2013-05-05 An ideal introduction to Einstein's general theory of relativity This unique textbook provides an accessible introduction to Einstein's general theory of relativity, a subject of breathtaking beauty and supreme importance in physics. With his trademark blend of wit and incisiveness, A. Zee guides readers from the fundamentals of Newtonian mechanics to the most exciting frontiers of research today, including de Sitter and anti-de Sitter spacetimes, Kaluza-Klein theory, and brane worlds. Unlike other books on Einstein gravity, this book emphasizes the action principle and group theory as guides in constructing physical theories. Zee treats various topics in a spiral style that is easy on beginners, and includes anecdotes from the history of physics that will appeal to students and experts alike. He takes a friendly approach to the required mathematics, yet does not shy away from more advanced mathematical topics such as differential forms. The extensive discussion of black holes includes rotating and extremal black holes and Hawking radiation. The ideal textbook for undergraduate and graduate students, Einstein Gravity in a Nutshell also provides an essential resource for professional physicists and is accessible to anyone familiar with classical mechanics and electromagnetism. It features numerous exercises as well as detailed appendices covering a multitude of topics not readily found elsewhere. Provides an accessible introduction to Einstein's general theory of relativity Guides readers from Newtonian mechanics to the frontiers of modern research Emphasizes symmetry and the Einstein-Hilbert action Covers topics not found in standard textbooks on Einstein gravity Includes interesting historical asides Features numerous exercises and detailed appendices Ideal for students, physicists, and scientifically minded lay readers Solutions manual (available only to teachers) |
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MODERN Definition & Meaning - Merriam-Webster
The meaning of MODERN is of, relating to, or characteristic of the present or the immediate past : contemporary. How to use modern in a sentence.
MODERN | English meaning - Cambridge Dictionary
MODERN definition: 1. designed and made using the most recent ideas and methods: 2. of the present or recent …
Modern - Wikipedia
Modernity, a loosely defined concept delineating a number of societal, economic and ideological features that contrast with "pre-modern" times or …
Modern - definition of modern by The Free Dictionary
Characteristic or expressive of recent times or the present; contemporary or up-to-date: a modern lifestyle; a modern way of thinking. 2. a. Of or …
