Quadratic Mappings and Clifford Algebras

Quadratic Mappings and Clifford Algebras
Author: Jacques Helmstetter
Publisher: Springer Science & Business Media
Total Pages: 512
Release: 2008-05-24
Genre: Mathematics
ISBN: 3764386061

After general properties of quadratic mappings over rings, the authors more intensely study quadratic forms, and especially their Clifford algebras. To this purpose they review the required part of commutative algebra, and they present a significant part of the theory of graded Azumaya algebras. Interior multiplications and deformations of Clifford algebras are treated with the most efficient methods.

Clifford Algebras: An Introduction

Clifford Algebras: An Introduction
Author: D. J. H. Garling
Publisher: Cambridge University Press
Total Pages: 209
Release: 2011-06-23
Genre: Mathematics
ISBN: 1107096383

A straightforward introduction to Clifford algebras, providing the necessary background material and many applications in mathematics and physics.

An Introduction to Clifford Algebras and Spinors

An Introduction to Clifford Algebras and Spinors
Author: Jayme Vaz Jr.
Publisher: Oxford University Press
Total Pages: 257
Release: 2016
Genre: Mathematics
ISBN: 0198782926

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.

The Algebraic and Geometric Theory of Quadratic Forms

The Algebraic and Geometric Theory of Quadratic Forms
Author: Richard S. Elman
Publisher: American Mathematical Soc.
Total Pages: 456
Release: 2008-07-15
Genre: Mathematics
ISBN: 9780821873229

This book is a comprehensive study of the algebraic theory of quadratic forms, from classical theory to recent developments, including results and proofs that have never been published. The book is written from the viewpoint of algebraic geometry and includes the theory of quadratic forms over fields of characteristic two, with proofs that are characteristic independent whenever possible. For some results both classical and geometric proofs are given. Part I includes classical algebraic theory of quadratic and bilinear forms and answers many questions that have been raised in the early stages of the development of the theory. Assuming only a basic course in algebraic geometry, Part II presents the necessary additional topics from algebraic geometry including the theory of Chow groups, Chow motives, and Steenrod operations. These topics are used in Part III to develop a modern geometric theory of quadratic forms.

Clifford Algebras and Dirac Operators in Harmonic Analysis

Clifford Algebras and Dirac Operators in Harmonic Analysis
Author: John E. Gilbert
Publisher: Cambridge University Press
Total Pages: 346
Release: 1991-07-26
Genre: Mathematics
ISBN: 9780521346542

The aim of this book is to unite the seemingly disparate topics of Clifford algebras, analysis on manifolds, and harmonic analysis. The authors show how algebra, geometry, and differential equations play a more fundamental role in Euclidean Fourier analysis. They then link their presentation of the Euclidean theory naturally to the representation theory of semi-simple Lie groups.

Geometric Algebra Computing

Geometric Algebra Computing
Author: Eduardo Bayro-Corrochano
Publisher: Springer Science & Business Media
Total Pages: 527
Release: 2010-05-19
Genre: Computers
ISBN: 1849961085

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.

Clifford Algebras and Spinors

Clifford Algebras and Spinors
Author: Pertti Lounesto
Publisher: Cambridge University Press
Total Pages: 352
Release: 2001-05-03
Genre: Mathematics
ISBN: 0521005515

This is the second edition of a popular work offering a unique introduction to Clifford algebras and spinors. The beginning chapters could be read by undergraduates; vectors, complex numbers and quaternions are introduced with an eye on Clifford algebras. The next chapters will also interest physicists, and include treatments of the quantum mechanics of the electron, electromagnetism and special relativity with a flavour of Clifford algebras. This edition has three new chapters, including material on conformal invariance and a history of Clifford algebras.

Essays in Mathematics and its Applications

Essays in Mathematics and its Applications
Author: Themistocles M. Rassias
Publisher: Springer
Total Pages: 659
Release: 2016-06-14
Genre: Mathematics
ISBN: 331931338X

This volume, dedicated to the eminent mathematician Vladimir Arnold, presents a collection of research and survey papers written on a large spectrum of theories and problems that have been studied or introduced by Arnold himself. Emphasis is given to topics relating to dynamical systems, stability of integrable systems, algebraic and differential topology, global analysis, singularity theory and classical mechanics. A number of applications of Arnold’s groundbreaking work are presented. This publication will assist graduate students and research mathematicians in acquiring an in-depth understanding and insight into a wide domain of research of an interdisciplinary nature.

The Algebraic Theory of Spinors and Clifford Algebras

The Algebraic Theory of Spinors and Clifford Algebras
Author: Claude Chevalley
Publisher: Springer Science & Business Media
Total Pages: 232
Release: 1996-12-13
Genre: Mathematics
ISBN: 9783540570639

In 1982, Claude Chevalley expressed three specific wishes with respect to the publication of his Works. First, he stated very clearly that such a publication should include his non technical papers. His reasons for that were two-fold. One reason was his life long commitment to epistemology and to politics, which made him strongly opposed to the view otherwise currently held that mathematics involves only half of a man. As he wrote to G. C. Rota on November 29th, 1982: "An important number of papers published by me are not of a mathematical nature. Some have epistemological features which might explain their presence in an edition of collected papers of a mathematician, but quite a number of them are concerned with theoretical politics ( . . . ) they reflect an aspect of myself the omission of which would, I think, give a wrong idea of my lines of thinking". On the other hand, Chevalley thought that the Collected Works of a mathematician ought to be read not only by other mathematicians, but also by historians of science.

Clifford Algebras with Numeric and Symbolic Computations

Clifford Algebras with Numeric and Symbolic Computations
Author: Rafal Ablamowicz
Publisher: Springer Science & Business Media
Total Pages: 328
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461581575

This edited survey book consists of 20 chapters showing application of Clifford algebra in quantum mechanics, field theory, spinor calculations, projective geometry, Hypercomplex algebra, function theory and crystallography. Many examples of computations performed with a variety of readily available software programs are presented in detail.