Author: S. A. Huggett
Publisher: Cambridge University Press
ISBN: 9780521456890
Category : Mathematics
Languages : en
Pages : 196
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Book Description
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.
Author: Roger Penrose
Publisher: Cambridge University Press
ISBN: 9780521337076
Category : Mathematics
Languages : en
Pages : 476
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Book Description
Volume 1 introduces and systematically develops the calculus in a first detailed exposition of this technique which provides shortcuts for some very tedious calculations.
Author: Rolf Berndt
Publisher: American Mathematical Society
ISBN: 1470476886
Category : Mathematics
Languages : en
Pages : 213
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Book Description
Symplectic geometry is a central topic of current research in mathematics. Indeed, symplectic methods are key ingredients in the study of dynamical systems, differential equations, algebraic geometry, topology, mathematical physics and representations of Lie groups. This book is a true introduction to symplectic geometry, assuming only a general background in analysis and familiarity with linear algebra. It starts with the basics of the geometry of symplectic vector spaces. Then, symplectic manifolds are defined and explored. In addition to the essential classic results, such as Darboux's theorem, more recent results and ideas are also included here, such as symplectic capacity and pseudoholomorphic curves. These ideas have revolutionized the subject. The main examples of symplectic manifolds are given, including the cotangent bundle, Kähler manifolds, and coadjoint orbits. Further principal ideas are carefully examined, such as Hamiltonian vector fields, the Poisson bracket, and connections with contact manifolds. Berndt describes some of the close connections between symplectic geometry and mathematical physics in the last two chapters of the book. In particular, the moment map is defined and explored, both mathematically and in its relation to physics. He also introduces symplectic reduction, which is an important tool for reducing the number of variables in a physical system and for constructing new symplectic manifolds from old. The final chapter is on quantization, which uses symplectic methods to take classical mechanics to quantum mechanics. This section includes a discussion of the Heisenberg group and the Weil (or metaplectic) representation of the symplectic group. Several appendices provide background material on vector bundles, on cohomology, and on Lie groups and Lie algebras and their representations. Berndt's presentation of symplectic geometry is a clear and concise introduction to the major methods and applications of the subject, and requires only a minimum of prerequisites. This book would be an excellent text for a graduate course or as a source for anyone who wishes to learn about symplectic geometry.
Author: Roger Penrose
Publisher: Cambridge University Press
ISBN: 9780521347860
Category : Mathematics
Languages : en
Pages : 516
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Book Description
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.
Author: Roger Penrose
Publisher: Cambridge University Press
ISBN: 9780521347860
Category : Science
Languages : en
Pages : 0
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Book Description
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. Twistors have, in recent years, attracted increasing attention as a mathematical tool and as a means of gaining new insights into the structure of physical laws. This volume also includes a comprehensive treatment of the conformal approach to space-time infinity with results on general-relativistic mass and angular momentum, a detailed spinorial classification of the full space-time curvature tensor, and an account of the geometry of null geodesics.
Author: Elie Cartan
Publisher: Courier Corporation
ISBN: 9780486640709
Category : Mathematics
Languages : en
Pages : 198
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Book Description
The French mathematician Élie Cartan (1869–1951) was one of the founders of the modern theory of Lie groups, a subject of central importance in mathematics and also one with many applications. In this volume, he describes the orthogonal groups, either with real or complex parameters including reflections, and also the related groups with indefinite metrics. He develops the theory of spinors (he discovered the general mathematical form of spinors in 1913) systematically by giving a purely geometrical definition of these mathematical entities; this geometrical origin makes it very easy to introduce spinors into Riemannian geometry, and particularly to apply the idea of parallel transport to these geometrical entities. The book is divided into two parts. The first is devoted to generalities on the group of rotations in n-dimensional space and on the linear representations of groups, and to the theory of spinors in three-dimensional space. Finally, the linear representations of the group of rotations in that space (of particular importance to quantum mechanics) are also examined. The second part is devoted to the theory of spinors in spaces of any number of dimensions, and particularly in the space of special relativity (Minkowski space). While the basic orientation of the book as a whole is mathematical, physicists will be especially interested in the final chapters treating the applications of spinors in the rotation and Lorentz groups. In this connection, Cartan shows how to derive the "Dirac" equation for any group, and extends the equation to general relativity. One of the greatest mathematicians of the 20th century, Cartan made notable contributions in mathematical physics, differential geometry, and group theory. Although a profound theorist, he was able to explain difficult concepts with clarity and simplicity. In this detailed, explicit treatise, mathematicians specializing in quantum mechanics will find his lucid approach a great value.
Author: Giulio Soliani
Publisher: World Scientific
ISBN: 9814513504
Category : Science
Languages : en
Pages : 837
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Book Description
This is the most up-to-date book on solitons and is divided into two parts. Part 1: Detailed introductory lectures on different aspects of solitons plus lectures on the mathematical aspects on this subject. Part 2: Is a collection of reprints on mathematical theories of solitons, solitons in field theory, solitons as particles and their properties, especially topological and physical properties. This book is aimed at a wide audience of physicists and mathematicians. It is an ideal reference book for young researchers and graduate students.
Author: Yasunori Fujii
Publisher: Cambridge University Press
ISBN: 1139436023
Category : Science
Languages : en
Pages : 258
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Book Description
A pedagogical overview of the theoretical ideas behind the cosmological constant problem, in particular the scalar-tensor theory, which is one of the most popular alternative theories of gravitation. Covering many developments in the field, including branes and quintessence, it will be an invaluable resource for graduate students and researchers alike.
Author: John L. Friedman
Publisher: Cambridge University Press
ISBN: 1107310601
Category : Science
Languages : en
Pages : 435
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Book Description
The masses of neutron stars are limited by an instability to gravitational collapse and an instability driven by gravitational waves limits their spin. Their oscillations are relevant to x-ray observations of accreting binaries and to gravitational wave observations of neutron stars formed during the coalescence of double neutron-star systems. This volume includes more than forty years of research to provide graduate students and researchers in astrophysics, gravitational physics and astronomy with the first self-contained treatment of the structure, stability and oscillations of rotating neutron stars. This monograph treats the equations of stellar equilibrium; key approximations, including slow rotation and perturbations of spherical and rotating stars; stability theory and its applications, from convective stability to the r-mode instability; and numerical methods for computing equilibrium configurations and the nonlinear evolution of their oscillations. The presentation of fundamental equations, results and applications is accessible to readers who do not need the detailed derivations.
Author: V. N. Gribov
Publisher: Cambridge University Press
ISBN: 1139441892
Category : Science
Languages : en
Pages : 311
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Book Description
This 2003 book is a rigorous introduction to the theory of complex angular momenta, based on the methods of field theory. This is an English translation of the famous lecture course given by Vladimir Gribov in 1969. Besides their historical significance, these lectures are highly relevant to modern research in theoretical physics.
