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# π Clifford Algebras and Spinors by A.A. Wessol, D.M. Pirro β pdf free

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This second edition of a popular and unique introduction to Clifford algebras and spinors has three new chapters. The beginning chapters cover the basics: vectors, complex numbers and quaternions are introduced with an eye on Clifford algebras. The next chapters, which will also interest physicists, include treatments of the quantum mechanics of the electron, electromagnetism and special relativity. A new classification of spinors is introduced, based on bilinear covariants of physical observables. This reveals a new class of spinors, residing among the Weyl, Majorana and Dirac spinors. Scalar products of spinors are categorized by involutory anti-automorphisms of Clifford algebras. This leads to the chessboard of automorphism groups of scalar products of spinors. On the algebraic side, Brauer/Wall groups and Witt rings are discussed, and on the analytic, Cauchy's integral formula is generalized to higher dimensions.

## About book:

## About file:

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- Series:
**London Mathematical Society Lecture Note Series** - Author:
**A.A. Wessol, D.M. Pirro** - Year:
**2001** - Publisher:
**Cambridge University Press** - Language:
**English** - ISBN:
**9780824705749,0824705742**

- File size:
**30 006 244** - Format:
**pdf**

Security code:

William Kingdon Clifford published the paper defining his "geometric algebras" in 1878, the year before his death. Clifford algebra is a generalisation to n-dimensional space of quaternions, which Hamilton used to represent scalars and vectors in real thr...

After a classical presentation of quadratic mappings and Clifford algebras over arbitrary rings (commutative, associative, with unit), other topics involve more original methods: interior multiplications allow an effective treatment of deformations of Cli...

Clifford algebras have become an indispensable tool for physicists at the cutting edge of theoretical investigations. Applications in physics range from special relativity and the rotating top at one end of the spectrum, to general relativity and Dirac's...

The use of Clifford algebras in mathematical physics and engineering has grown rapidly in recent years. Whereas other developments have privileged a geometric approach, the author uses an algebraic approach which can be introduced as a tensor product of q...

This book reflects the growing interest in the theory of Clifford algebras and their applications. The author has reworked his previous book on this subject, Topological Geometry, and has expanded and added material. As in the previous version, the author...

This volume contains selected papers presented at the Second Workshop on Clifford Algebras and their Applications in Mathematical Physics. These papers range from various algebraic and analytic aspects of Clifford algebras to applications in, for example,...

Quadratic Algebras, Clifford Algebras, and Arithmetic Forms introduces mathematicians to the large and dynamic area of algebras and forms over commutative rings. The book begins very elementary and progresses gradually in its degree of difficulty. Topics ...

Clifford algebras are assuming now an increasing role in theoretical physics. Some of them predominantly larger ones are used in elementary particle theory, especially for a unification of the fundamental interactions. The smaller ones are promoted in mor...

The topic is clear from the title. The author of this monograph has attempted to be at once as clear and as complete as possible, and to serve the needs both of mathematicians and of physicists. For all the effort he has given to (the very French concepti...

Convexity is a simple idea that manifests itself in a surprising variety of places. This fertile field has an immensely rich structure and numerous applications. Barvinok demonstrates that simplicity, intuitive appeal, and the universality of applications...

The Erd s problem asks, What is the smallest possible number of distinct distances between points of a large finite subset of the Euclidean space in dimensions two and higher? The main goal of this book is to introduce the reader to the techniques, ideas,...

The past two decades have brought explosive growth in 4-manifold theory. Many books are currently appearing that approach the topic from viewpoints such as gauge theory or algebraic geometry. This volume, however, offers an exposition from a topological p...

In this paper, the author studies all the elliptic integrable systems, in the sense of C, that is to say, the family of all the $m$-th elliptic integrable systems associated to a $k^\prime$-symmetric space $N=G/G_0$. The author describes the geometry behi...

J$-holomorphic curves revolutionized the study of symplectic geometry when Gromov first introduced them in 1985. Through quantum cohomology, these curves are now linked to many of the most exciting new ideas in mathematical physics. This book presents the...

This book is based on lectures given at Stanford University in 2009. The purpose of the lectures and of the book is to give an introductory overview of how to use Ricci flow and Ricci flow with surgery to establish the Poincare Conjecture and the more gen...

How many dimensions does our universe require for a comprehensive physical description? In 1905, PoincarΓ© argued philosophically about the necessity of the three familiar dimensions, while recent research is based on 11 dimensions or even 23 dimensions. T...

This book deals first with Haar bases, Faber bases and Faber frames for weighted function spaces on the real line and the plane. It extends results in the author's book, "Bases in Function Spaces, Sampling, Discrepancy, Numerical Integration" (EMS, 2010),...

This book investigates several duality approaches for vector optimization problems, while also comparing them. Special attention is paid to duality for linear vector optimization problems, for which a vector dual that avoids the shortcomings of the classi...

This book offers a systematic introduction to the optimal stochastic control theory via the dynamic programming principle, which is a powerful tool to analyze control problems.First we consider completely observable control problems with finite horizons. ...