Download or read book Twistor and Killing Spinors in Lorentzian Geometry written by Helga Baum and published by . This book was released on 2000 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometry Lie Theory and Applications written by Sigbjørn Hervik and published by Springer Nature. This book was released on 2022-02-07 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of contributions from the participants of the Abel Symposium 2019 held in Ålesund, Norway. It was centered about applications of the ideas of symmetry and invariance, including equivalence and deformation theory of geometric structures, classification of differential invariants and invariant differential operators, integrability analysis of equations of mathematical physics, progress in parabolic geometry and mathematical aspects of general relativity. The chapters are written by leading international researchers, and consist of both survey and research articles. The book gives the reader an insight into the current research in differential geometry and Lie theory, as well as applications of these topics, in particular to general relativity and string theory.
Download or read book Spinors In Physics And Geometry written by Giuseppe Furlan and published by World Scientific. This book was released on 1988-11-01 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This conference brought together physicists and mathematicians working on spinors, which have played an important role in recent research on supersymmetry, Kaluza-Klein theories, twistors and general relativity.
Download or read book Spinors in Four Dimensional Spaces written by Gerardo F. Torres del Castillo and published by Springer Science & Business Media. This book was released on 2010-07-23 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: Without using the customary Clifford algebras frequently studied in connection with the representations of orthogonal groups, this book gives an elementary introduction to the two-component spinor formalism for four-dimensional spaces with any signature. Some of the useful applications of four-dimensional spinors, such as Yang–Mills theory, are derived in detail using illustrative examples. Spinors in Four-Dimensional Spaces is aimed at graduate students and researchers in mathematical and theoretical physics interested in the applications of the two-component spinor formalism in any four-dimensional vector space or Riemannian manifold with a definite or indefinite metric tensor. This systematic and self-contained book is suitable as a seminar text, a reference book, and a self-study guide.
Download or read book A Note on Twistor Spinors with Zeros in Lorentzian Geometry written by Felipe Leitner and published by . This book was released on 2004 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Symmetries and Overdetermined Systems of Partial Differential Equations written by Michael Eastwood and published by Springer Science & Business Media. This book was released on 2009-04-23 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: This three-week summer program considered the symmetries preserving various natural geometric structures. There are two parts to the proceedings. The articles in the first part are expository but all contain significant new material. The articles in the second part are concerned with original research. All articles were thoroughly refereed and the range of interrelated work ensures that this will be an extremely useful collection.
Download or read book Supersymmetric Field Theories written by Sergio Cecotti and published by Cambridge University Press. This book was released on 2015-01-08 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: Adopting an elegant geometrical approach, this advanced pedagogical text describes deep and intuitive methods for understanding the subtle logic of supersymmetry while avoiding lengthy computations. The book describes how complex results and formulae obtained using other approaches can be significantly simplified when translated to a geometric setting. Introductory chapters describe geometric structures in field theory in the general case, while detailed later chapters address specific structures such as parallel tensor fields, G-structures, and isometry groups. The relationship between structures in supergravity and periodic maps of algebraic manifolds, Kodaira–Spencer theory, modularity, and the arithmetic properties of supergravity are also addressed. Relevant geometric concepts are introduced and described in detail, providing a self-contained toolkit of useful techniques, formulae and constructions. Covering all the material necessary for the application of supersymmetric field theories to fundamental physical questions, this is an outstanding resource for graduate students and researchers in theoretical physics.
Download or read book Further Advances in Twistor Theory written by L.J. Mason and published by CRC Press. This book was released on 2023-05-31 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Global Differential Geometry written by Christian Bär and published by Springer Science & Business Media. This book was released on 2011-12-18 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of well-written surveys provided by experts in Global Differential Geometry to give an overview over recent developments in Riemannian Geometry, Geometric Analysis and Symplectic Geometry. The papers are written for graduate students and researchers with a general interest in geometry, who want to get acquainted with the current trends in these central fields of modern mathematics.
Download or read book Conformal Differential Geometry written by Helga Baum and published by Springer Science & Business Media. This book was released on 2011-01-28 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conformal invariants (conformally invariant tensors, conformally covariant differential operators, conformal holonomy groups etc.) are of central significance in differential geometry and physics. Well-known examples of such operators are the Yamabe-, the Paneitz-, the Dirac- and the twistor operator. The aim of the seminar was to present the basic ideas and some of the recent developments around Q-curvature and conformal holonomy. The part on Q-curvature discusses its origin, its relevance in geometry, spectral theory and physics. Here the influence of ideas which have their origin in the AdS/CFT-correspondence becomes visible. The part on conformal holonomy describes recent classification results, its relation to Einstein metrics and to conformal Killing spinors, and related special geometries.
Download or read book Global Analysis and Harmonic Analysis written by Jean-Pierre Bourguignon and published by Société Mathématique de France. This book was released on 2000 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the proceedings of a meeting intended to gather researchers working in the fields of harmonic analysis and global analysis to discuss some questions of common interest. About twenty talks covered the principal topics, illustrating the recent interactions between these two fields. The meeting started with a survey on spin geometry and was followed by talks on the spectrum of the Dirac operator in hyperbolic, Kahlerian and pseudo-Riemannian geometry. Different aspects of representation theory were discussed: Schubert cells, unitary representations with reflection symmetry, gradient operators, and Poisson transformations. Another series of talks was devoted to the systematic use of representation theory in global analysis; in particular on the Bernstein-Gelfand-Gelfand sequences in parabolic geometry, the construction of conformally covariant operators, and some refinements of the Kato inequality in Riemannian geometry. Various presentations ranging from general relativity to harmonic maps, by way of $4$-dimensional geometry/topology, Seiberg-Witten theory and the index theorem in $2$-dimensional hyperbolic geometry illustrated the diversity of applications of techniques from harmonic analysis.
Download or read book Applied Differential Geometry written by Vladimir G. Ivancevic and published by World Scientific. This book was released on 2007 with total page 1346 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level monographic textbook treats applied differential geometry from a modern scientific perspective. Co-authored by the originator of the world's leading human motion simulator ? ?Human Biodynamics Engine?, a complex, 264-DOF bio-mechanical system, modeled by differential-geometric tools ? this is the first book that combines modern differential geometry with a wide spectrum of applications, from modern mechanics and physics, via nonlinear control, to biology and human sciences. The book is designed for a two-semester course, which gives mathematicians a variety of applications for their theory and physicists, as well as other scientists and engineers, a strong theory underlying their models.
Download or read book Recent Developments in Pseudo Riemannian Geometry written by Dmitriĭ Vladimirovich Alekseevskiĭ and published by European Mathematical Society. This book was released on 2008 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to and survey of recent developments in pseudo-Riemannian geometry, including applications in mathematical physics, by leading experts in the field. Topics covered are: Classification of pseudo-Riemannian symmetric spaces Holonomy groups of Lorentzian and pseudo-Riemannian manifolds Hypersymplectic manifolds Anti-self-dual conformal structures in neutral signature and integrable systems Neutral Kahler surfaces and geometric optics Geometry and dynamics of the Einstein universe Essential conformal structures and conformal transformations in pseudo-Riemannian geometry The causal hierarchy of spacetimes Geodesics in pseudo-Riemannian manifolds Lorentzian symmetric spaces in supergravity Generalized geometries in supergravity Einstein metrics with Killing leaves The book is addressed to advanced students as well as to researchers in differential geometry, global analysis, general relativity and string theory. It shows essential differences between the geometry on manifolds with positive definite metrics and on those with indefinite metrics, and highlights the interesting new geometric phenomena, which naturally arise in the indefinite metric case. The reader finds a description of the present state of the art in the field as well as open problems, which can stimulate further research.
Download or read book Geometrical Dynamics of Complex Systems written by Vladimir G. Ivancevic and published by Taylor & Francis. This book was released on 2006-01-18 with total page 856 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometrical Dynamics of Complex Systems is a graduate-level monographic textbook. Itrepresentsacomprehensiveintroductionintorigorousgeometrical dynamicsofcomplexsystemsofvariousnatures. By'complexsystems', inthis book are meant high-dimensional nonlinear systems, which can be (but not necessarily are) adaptive. This monograph proposes a uni?ed geometrical - proachtodynamicsofcomplexsystemsofvariouskinds: engineering, physical, biophysical, psychophysical, sociophysical, econophysical, etc. As their names suggest, all these multi-input multi-output (MIMO) systems have something in common: the underlying physics. However, instead of dealing with the pop- 1 ular 'soft complexity philosophy', we rather propose a rigorous geometrical and topological approach. We believe that our rigorous approach has much greater predictive power than the soft one. We argue that science and te- nology is all about prediction and control. Observation, understanding and explanation are important in education at undergraduate level, but after that it should be all prediction and control. The main objective of this book is to show that high-dimensional nonlinear systems and processes of 'real life' can be modelled and analyzed using rigorous mathematics, which enables their complete predictability and controllability, as if they were linear systems. It is well-known that linear systems, which are completely predictable and controllable by de?nition - live only in Euclidean spaces (of various - mensions). They are as simple as possible, mathematically elegant and fully elaborated from either scienti?c or engineering side. However, in nature, no- ing is linear. In reality, everything has a certain degree of nonlinearity, which means: unpredictability, with subsequent uncontrollability.
Download or read book Theory Of Spinors An Introduction written by Moshe Carmeli and published by World Scientific Publishing Company. This book was released on 2000-04-12 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spinors are used extensively in physics. It is widely accepted that they are more fundamental than tensors, and the easy way to see this is through the results obtained in general relativity theory by using spinors — results that could not have been obtained by using tensor methods only.The foundation of the concept of spinors is groups; spinors appear as representations of groups. This textbook expounds the relationship between spinors and representations of groups. As is well known, spinors and representations are both widely used in the theory of elementary particles.The authors present the origin of spinors from representation theory, but nevertheless apply the theory of spinors to general relativity theory, and part of the book is devoted to curved space-time applications.Based on lectures given at Ben Gurion University, this textbook is intended for advanced undergraduate and graduate students in physics and mathematics, as well as being a reference for researchers.
Download or read book Handbook of Pseudo Riemannian Geometry and Supersymmetry written by Vicente Cortés and published by European Mathematical Society. This book was released on 2010 with total page 972 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this handbook is to give an overview of some recent developments in differential geometry related to supersymmetric field theories. The main themes covered are: Special geometry and supersymmetry Generalized geometry Geometries with torsion Para-geometries Holonomy theory Symmetric spaces and spaces of constant curvature Conformal geometry Wave equations on Lorentzian manifolds D-branes and K-theory The intended audience consists of advanced students and researchers working in differential geometry, string theory, and related areas. The emphasis is on geometrical structures occurring on target spaces of supersymmetric field theories. Some of these structures can be fully described in the classical framework of pseudo-Riemannian geometry. Others lead to new concepts relating various fields of research, such as special Kahler geometry or generalized geometry.
Download or read book Spinors and Space Time Volume 2 Spinor and Twistor Methods in Space Time Geometry written by Roger Penrose and published by Cambridge University Press. This book was released on 1984 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the two volumes that comprise this work Roger Penrose and Wolfgang Rindler introduce the calculus of 2-spinors and the theory of twistors, and discuss in detail how these powerful and elegant methods may be used to elucidate the structure and properties of space-time. In volume 1, Two-spinor calculus and relativistic fields, the calculus of 2-spinors is introduced and developed. Volume 2, Spinor and twistor methods in space-time geometry, introduces the theory of twistors, and studies in detail how the theory of twistors and 2-spinors can be applied to the study of space-time. This work will be of great value to all those studying relativity, differential geometry, particle physics and quantum field theory from beginning graduate students to experts in these fields.
