This book provides a self-contained overview of the role of conformal groups in geometry and mathematical physics. It features a careful development of the material, from the basics of Clifford algebras to more advanced topics. Each chapter covers a specific aspect of conformal groups and conformal spin geometry. All major concepts are introduced and followed by detailed descriptions and definitions, and a comprehensive bibliography and index round out the work. Rich in exercises that are accompanied by full proofs and many hints, the book will be ideal as a course text or self-study volume for senior undergraduates and graduate students.
This book provides a self-contained overview of the role of conformal groups in geometry and mathematical physics. It features a careful development of the material, from the basics of Clifford algebras to more advanced topics. Each chapter covers a specific aspect of conformal groups and conformal spin geometry. All major concepts are introduced and followed by detailed descriptions and definitions, and a comprehensive bibliography and index round out the work. Rich in exercises that are accompanied by full proofs and many hints, the book will be ideal as a course text or self-study volume for senior undergraduates and graduate students.
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.
This book explores the Lipschitz spinorial groups (versor, pinor, spinor and rotor groups) of a real non-degenerate orthogonal geometry (or orthogonal geometry, for short) and how they relate to the group of isometries of that geometry. After a concise mathematical introduction, it offers an axiomatic presentation of the geometric algebra of an orthogonal geometry. Once it has established the language of geometric algebra (linear grading of the algebra; geometric, exterior and interior products; involutions), it defines the spinorial groups, demonstrates their relation to the isometry groups, and illustrates their suppleness (geometric covariance) with a variety of examples. Lastly, the book provides pointers to major applications, an extensive bibliography and an alphabetic index. Combining the characteristics of a self-contained research monograph and a state-of-the-art survey, this book is a valuable foundation reference resource on applications for both undergraduate and graduate students.
This useful text offers new insights and solutions for the development of theorems, algorithms and advanced methods for real-time applications across a range of disciplines. Its accessible style is enhanced by examples, figures and experimental analysis.
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.
The application of geometric algebra to the engineering sciences is a young, active subject of research. The promise of this field is that the mathematical structure of geometric algebra together with its descriptive power will result in intuitive and more robust algorithms. This book examines all aspects essential for a successful application of geometric algebra: the theoretical foundations, the representation of geometric constraints, and the numerical estimation from uncertain data. Formally, the book consists of two parts: theoretical foundations and applications. The first part includes chapters on random variables in geometric algebra, linear estimation methods that incorporate the uncertainty of algebraic elements, and the representation of geometry in Euclidean, projective, conformal and conic space. The second part is dedicated to applications of geometric algebra, which include uncertain geometry and transformations, a generalized camera model, and pose estimation. Graduate students, scientists, researchers and practitioners will benefit from this book. The examples given in the text are mostly recent research results, so practitioners can see how to apply geometric algebra to real tasks, while researchers note starting points for future investigations. Students will profit from the detailed introduction to geometric algebra, while the text is supported by the author's visualization software, CLUCalc, freely available online, and a website that includes downloadable exercises, slides and tutorials.
A moving portrait of Africa from Polands most celebrated foreign correspondent - a masterpiece from a modern master. Famous for being in the wrong places at just the right times, Ryszard Kapuscinski arrived in Africa in 1957, at the beginning of the end of colonial rule - the &"sometimes dramatic and painful, sometimes enjoyable and jubilant&" rebirth of a continent.The Shadow of the Sunsums up the authors experiences (&"the record of a 40-year marriage&") in this place that became the central obsession of his remarkable career. From the hopeful years of independence through the bloody disintegration of places like Nigeria, Rwanda and Angola, Kapuscinski recounts great social and political changes through the prism of the ordinary African. He examines the rough-and-ready physical world and identifies the true geography of Africa: a little-understood spiritual universe, an African way of being. He looks also at Africa in the wake of two epoch-making changes: the arrival of AIDS and the definitive departure of the white man. Kapuscinskis rare humanity invests his subjects with a grandeur and a dignity unmatched by any other writer on the Third World, and his unique ability to discern the universal in the particular has never been more powerfully displayed than in this work. From the Trade Paperback edition.
This work is unique compared to the existing literature. It is very didactical and accessible to both students and researchers, without neglecting the formal character and the deep algebraic completeness of the topic along with its physical applications.
