The Penrose Transform

Author : Robert J. Baston,Michael G. Eastwood
Publisher : Courier Dover Publications
Page : 257 pages
File Size : 41,5 Mb
Release : 2016-11-16
Category : Mathematics
ISBN : 9780486797298

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The Penrose Transform by Robert J. Baston,Michael G. Eastwood Pdf

"Brings to the reader a huge amount of information, well organized and condensed into less than two hundred pages." — Mathematical Reviews In recent decades twistor theory has become an important focus for students of mathematical physics. Central to twistor theory is the geometrical transform known as the Penrose transform, named for its groundbreaking developer. Geared toward students of physics and mathematics, this advanced text explores the Penrose transform and presupposes no background in twistor theory and a minimal familiarity with representation theory. An introductory chapter sketches the development of the Penrose transform, followed by reviews of Lie algebras and flag manifolds, representation theory and homogeneous vector bundles, and the Weyl group and the Bott-Borel-Weil theorem. Succeeding chapters explore the Penrose transform in terms of the Bernstein-Gelfand-Gelfand resolution, followed by worked examples, constructions of unitary representations, and module structures on cohomology. The treatment concludes with a review of constructions and suggests further avenues for research.

Author : Michael G. Eastwood,Joseph Albert Wolf,Roger Zierau,American Mathematical Society,Institute of Mathematical Statistics
Publisher : American Mathematical Soc.
Page : 259 pages
File Size : 48,6 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821851760

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The Penrose Transform and Analytic Cohomology in Representation Theory by Michael G. Eastwood,Joseph Albert Wolf,Roger Zierau,American Mathematical Society,Institute of Mathematical Statistics Pdf

This book contains refereed papers presented at the AMS-IMS-SIAM Summer Research Conference on the Penrose Transform and Analytic Cohomology in Representation Theory held in the summer of 1992 at Mount Holyoke College. The conference brought together some of the top experts in representation theory and differential geometry. One of the issues explored at the conference was the fact that various integral transforms from representation theory, complex integral geometry, and mathematical physics appear to be instances of the same general construction, which is sometimes called the Penrose transform''. There is considerable scope for further research in this area, and this book would serve as an excellent introduction.

Author : Lionel J. Mason,L. P. Hughston
Publisher : Unknown
Page : 399 pages
File Size : 45,7 Mb
Release : 1990
Category : Twistor theory
ISBN : 0608035998

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Further Advances in Twistor Theory by Lionel J. Mason,L. P. Hughston Pdf

Author : Gen Komatsu,Masatake Kuranishi
Publisher : Springer Science & Business Media
Page : 322 pages
File Size : 40,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461221661

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Analysis and Geometry in Several Complex Variables by Gen Komatsu,Masatake Kuranishi Pdf

This volume consists of a collection of articles for the proceedings of the 40th Taniguchi Symposium Analysis and Geometry in Several Complex Variables held in Katata, Japan, on June 23-28, 1997. Since the inhomogeneous Cauchy-Riemann equation was introduced in the study of Complex Analysis of Several Variables, there has been strong interaction between Complex Analysis and Real Analysis, in particular, the theory of Partial Differential Equations. Problems in Complex Anal ysis stimulate the development of the PDE theory which subsequently can be applied to Complex Analysis. This interaction involves Differen tial Geometry, for instance, via the CR structure modeled on the induced structure on the boundary of a complex manifold. Such structures are naturally related to the PDE theory. Differential Geometric formalisms are efficiently used in settling problems in Complex Analysis and the results enrich the theory of Differential Geometry. This volume focuses on the most recent developments in this inter action, including links with other fields such as Algebraic Geometry and Theoretical Physics. Written by participants in the Symposium, this vol ume treats various aspects of CR geometry and the Bergman kernel/ pro jection, together with other major subjects in modern Complex Analysis. We hope that this volume will serve as a resource for all who are interested in the new trends in this area. We would like to express our gratitude to the Taniguchi Foundation for generous financial support and hospitality. We would also like to thank Professor Kiyosi Ito who coordinated the organization of the symposium.

Author : T. N. Bailey,R. J. Baston
Publisher : Cambridge University Press
Page : 395 pages
File Size : 40,8 Mb
Release : 1990-08-23
Category : Mathematics
ISBN : 9780521397834

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Twistors in Mathematics and Physics by T. N. Bailey,R. J. Baston Pdf

This 1990 collection of review articles covers the considerable progress made in a wide range of applications of twistor theory.

Author : Eric Todd Quinto
Publisher : American Mathematical Soc.
Page : 274 pages
File Size : 40,9 Mb
Release : 2001
Category : Radon transforms
ISBN : 9780821821350

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Radon Transforms and Tomography by Eric Todd Quinto Pdf

One of the most exciting features of the fields of Radon transforms and tomography is the strong relationship between high-level pure mathematics and applications to areas such as medical imaging and industrial nondestructive evaluation. The proceedings featured in this volume bring together fundamental research articles in the major areas of Radon transforms and tomography. This volume includes expository papers that are of special interest to beginners as well as advanced researchers. Topics include local tomography and wavelets, Lambda tomography and related methods, tomographic methods in RADAR, ultrasound, Radon transforms and differential equations, and the Pompeiu problem. The major themes in Radon transforms and tomography are represented among the research articles. Pure mathematical themes include vector tomography, microlocal analysis, twistor theory, Lie theory, wavelets, harmonic analysis, and distribution theory. The applied articles employ high-quality pure mathematics to solve important practical problems. Effective scanning geometries are developed and tested for a NASA wind tunnel. Algorithms for limited electromagnetic tomographic data and for impedance imaging are developed and tested. Range theorems are proposed to diagnose problems with tomography scanners. Principles are given for the design of X-ray tomography reconstruction algorithms, and numerical examples are provided. This volume offers readers a comprehensive source of fundamental research useful to both beginners and advanced researchers in the fields.

Author : Andrew Markoe
Publisher : Cambridge University Press
Page : 358 pages
File Size : 54,7 Mb
Release : 2006-01-23
Category : Mathematics
ISBN : 9780521793476

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Analytic Tomography by Andrew Markoe Pdf

This study contains elementary introductions to properties of the Radon transform plus coverage of more advanced topics.

Author : R. Delanghe,F. Sommen,V. Soucek
Publisher : Springer Science & Business Media
Page : 501 pages
File Size : 45,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401129220

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Clifford Algebra and Spinor-Valued Functions by R. Delanghe,F. Sommen,V. Soucek Pdf

This volume describes the substantial developments in Clifford analysis which have taken place during the last decade and, in particular, the role of the spin group in the study of null solutions of real and complexified Dirac and Laplace operators. The book has six main chapters. The first two (Chapters 0 and I) present classical results on real and complex Clifford algebras and show how lower-dimensional real Clifford algebras are well-suited for describing basic geometric notions in Euclidean space. Chapters II and III illustrate how Clifford analysis extends and refines the computational tools available in complex analysis in the plane or harmonic analysis in space. In Chapter IV the concept of monogenic differential forms is generalized to the case of spin-manifolds. Chapter V deals with analysis on homogeneous spaces, and shows how Clifford analysis may be connected with the Penrose transform. The volume concludes with some Appendices which present basic results relating to the algebraic and analytic structures discussed. These are made accessible for computational purposes by means of computer algebra programmes written in REDUCE and are contained on an accompanying floppy disk.

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
Page : 639 pages
File Size : 51,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401512794

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Encyclopaedia of Mathematics by Michiel Hazewinkel Pdf

This is the second supplementary volume to Kluwer's highly acclaimed eleven-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing eleven volumes, and together these twelve volumes represent the most authoritative, comprehensive and up-to-date Encyclopaedia of Mathematics available.

Author : R. S. Ward,Raymond O'Neil Wells (Jr.)
Publisher : Cambridge University Press
Page : 534 pages
File Size : 40,9 Mb
Release : 1990
Category : Mathematics
ISBN : 052142268X

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Twistor Geometry and Field Theory by R. S. Ward,Raymond O'Neil Wells (Jr.) Pdf

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.

Author : Mark Green,Phillip Griffiths,Matt Kerr
Publisher : American Mathematical Soc.
Page : 145 pages
File Size : 43,6 Mb
Release : 2014-08-12
Category : Mathematics
ISBN : 9780821898574

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Special Values of Automorphic Cohomology Classes by Mark Green,Phillip Griffiths,Matt Kerr Pdf

The authors study the complex geometry and coherent cohomology of nonclassical Mumford-Tate domains and their quotients by discrete groups. Their focus throughout is on the domains which occur as open -orbits in the flag varieties for and , regarded as classifying spaces for Hodge structures of weight three. In the context provided by these basic examples, the authors formulate and illustrate the general method by which correspondence spaces give rise to Penrose transforms between the cohomologies of distinct such orbits with coefficients in homogeneous line bundles.

Author : Prof. Dr. Francisco Bulnes
Publisher : Scientific Research Publishing, Inc. USA
Page : 195 pages
File Size : 53,6 Mb
Release : 2016-06-08
Category : Mathematics
ISBN : 9781618961402

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Integral Geometry Methods in the Geometrical Langlands Program by Prof. Dr. Francisco Bulnes Pdf

The book is divided on the studied aspects in integral geometry and that are of interest in field theory, at least, to the solution or obtaining of integrals to the field equations corresponding to the moduli stacks planted. In the chapters 1, 2, 3, 4, are exposed the generalizations of the Penrose transforms with a good D-modules theory in the derived categories context and their deformations. In the chapters 5, and 6, are exposed and discussed the different classification problems and their implications in the differential operators to the field equations. Finally, in the chapters 7, and 8 are exposed the aspects of the geometrical ramification of field ramification going behold the holomorphicity. In the end of the book are included several research exercises that can be discussed and exposed inside postgraduate courses in derived geometry or related as derived categories or categories on commutative and non-commutative rings.

Author : Giampiero Esposito
Publisher : Springer Science & Business Media
Page : 216 pages
File Size : 54,9 Mb
Release : 2006-04-11
Category : Science
ISBN : 9780306471186

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Complex General Relativity by Giampiero Esposito Pdf

This book is written for theoretical and mathematical physicists and mat- maticians interested in recent developments in complex general relativity and their application to classical and quantum gravity. Calculations are presented by paying attention to those details normally omitted in research papers, for pedagogical r- sons. Familiarity with fibre-bundle theory is certainly helpful, but in many cases I only rely on two-spinor calculus and conformally invariant concepts in gravitational physics. The key concepts the book is devoted to are complex manifolds, spinor techniques, conformal gravity, ?-planes, ?-surfaces, Penrose transform, complex 3 1 – – space-time models with non-vanishing torsion, spin- fields and spin- potentials. 2 2 Problems have been inserted at the end, to help the reader to check his und- standing of these topics. Thus, I can find at least four reasons for writing yet another book on spinor and twistor methods in general relativity: (i) to write a textbook useful to - ginning graduate students and research workers, where two-component spinor c- culus is the unifying mathematical language.

Author : Mark Green, Phillip Griffiths,Matt Kerr
Publisher : American Mathematical Soc.
Page : 314 pages
File Size : 42,8 Mb
Release : 2013-11-05
Category : Mathematics
ISBN : 9781470410124

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Hodge Theory, Complex Geometry, and Representation Theory by Mark Green, Phillip Griffiths,Matt Kerr Pdf

This monograph presents topics in Hodge theory and representation theory, two of the most active and important areas in contemporary mathematics. The underlying theme is the use of complex geometry to understand the two subjects and their relationships to one another--an approach that is complementary to what is in the literature. Finite-dimensional representation theory and complex geometry enter via the concept of Hodge representations and Hodge domains. Infinite-dimensional representation theory, specifically the discrete series and their limits, enters through the realization of these representations through complex geometry as pioneered by Schmid, and in the subsequent description of automorphic cohomology. For the latter topic, of particular importance is the recent work of Carayol that potentially introduces a new perspective in arithmetic automorphic representation theory. The present work gives a treatment of Carayol's work, and some extensions of it, set in a general complex geometric framework. Additional subjects include a description of the relationship between limiting mixed Hodge structures and the boundary orbit structure of Hodge domains, a general treatment of the correspondence spaces that are used to construct Penrose transforms and selected other topics from the recent literature. A co-publication of the AMS and CBMS.

Author : L.J. Mason,P.Z. Kobak,L. Hughston,K. Pulverer
Publisher : CRC Press
Page : 436 pages
File Size : 55,8 Mb
Release : 2001-03-15
Category : Mathematics
ISBN : 1584880473

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Further Advances in Twistor Theory by L.J. Mason,P.Z. Kobak,L. Hughston,K. Pulverer Pdf

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