An Introduction to Clifford Algebras and Spinors - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Introduction to Clifford Algebras and Spinors write by Jayme Vaz Jr.. This book was released on 2016. An Introduction to Clifford Algebras and Spinors available in PDF, EPUB and Kindle. 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.
Clifford Algebras: An Introduction
Clifford Algebras: An Introduction - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Clifford Algebras: An Introduction write by D. J. H. Garling. This book was released on 2011-06-23. Clifford Algebras: An Introduction available in PDF, EPUB and Kindle. A straightforward introduction to Clifford algebras, providing the necessary background material and many applications in mathematics and physics.
Clifford Algebra to Geometric Calculus
Clifford Algebra to Geometric Calculus - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Clifford Algebra to Geometric Calculus write by David Hestenes. This book was released on 1984. Clifford Algebra to Geometric Calculus available in PDF, EPUB and Kindle. Matrix algebra has been called "the arithmetic of higher mathematics" [Be]. We think the basis for a better arithmetic has long been available, but its versatility has hardly been appreciated, and it has not yet been integrated into the mainstream of mathematics. We refer to the system commonly called 'Clifford Algebra', though we prefer the name 'Geometric Algebra' suggested by Clifford himself. Many distinct algebraic systems have been adapted or developed to express geometric relations and describe geometric structures. Especially notable are those algebras which have been used for this purpose in physics, in particular, the system of complex numbers, the quaternions, matrix algebra, vector, tensor and spinor algebras and the algebra of differential forms. Each of these geometric algebras has some significant advantage over the others in certain applications, so no one of them provides an adequate algebraic structure for all purposes of geometry and physics. At the same time, the algebras overlap considerably, so they provide several different mathematical representations for individual geometrical or physical ideas.
Clifford Algebras and Lie Theory
Clifford Algebras and Lie Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Clifford Algebras and Lie Theory write by Eckhard Meinrenken. This book was released on 2013-02-28. Clifford Algebras and Lie Theory available in PDF, EPUB and Kindle. This monograph provides an introduction to the theory of Clifford algebras, with an emphasis on its connections with the theory of Lie groups and Lie algebras. The book starts with a detailed presentation of the main results on symmetric bilinear forms and Clifford algebras. It develops the spin groups and the spin representation, culminating in Cartan’s famous triality automorphism for the group Spin(8). The discussion of enveloping algebras includes a presentation of Petracci’s proof of the Poincaré–Birkhoff–Witt theorem. This is followed by discussions of Weil algebras, Chern--Weil theory, the quantum Weil algebra, and the cubic Dirac operator. The applications to Lie theory include Duflo’s theorem for the case of quadratic Lie algebras, multiplets of representations, and Dirac induction. The last part of the book is an account of Kostant’s structure theory of the Clifford algebra over a semisimple Lie algebra. It describes his “Clifford algebra analogue” of the Hopf–Koszul–Samelson theorem, and explains his fascinating conjecture relating the Harish-Chandra projection for Clifford algebras to the principal sl(2) subalgebra. Aside from these beautiful applications, the book will serve as a convenient and up-to-date reference for background material from Clifford theory, relevant for students and researchers in mathematics and physics.
Quaternions, Clifford Algebras and Relativistic Physics
Quaternions, Clifford Algebras and Relativistic Physics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Quaternions, Clifford Algebras and Relativistic Physics write by Patrick R. Girard. This book was released on 2007-06-25. Quaternions, Clifford Algebras and Relativistic Physics available in PDF, EPUB and Kindle. The use of Clifford algebras in mathematical physics and engineering has grown rapidly in recent years. Whereas other developments have privileged a geometric approach, this book uses an algebraic approach that can be introduced as a tensor product of quaternion algebras and provides a unified calculus for much of physics. It proposes a pedagogical introduction to this new calculus, based on quaternions, with applications mainly in special relativity, classical electromagnetism, and general relativity.
