Geometric Algebra and Applications to Physics: a book by Venzo de Sabbata and Bidyut Kumar Datta

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Product Description

Bringing geometric algebra to the mainstream of physics pedagogy, Geometric Algebra and Applications to Physics not only presents geometric algebra as a discipline within mathematical physics, but the book also shows how geometric algebra can be applied to numerous fundamental problems in physics, especially in experimental situations.

This reference begins with several chapters that present the mathematical fundamentals of geometric algebra. It introduces the essential features of postulates and their underlying framework; bivectors, multivectors, and their operators; spinor and Lorentz rotations; and Clifford algebra. The book also extends some of these topics into three dimensions. Subsequent chapters apply these fundamentals to various common physical scenarios. The authors show how Maxwell’s equations can be expressed and manipulated via space-time algebra and how geometric algebra reveals electromagnetic waves’ states of polarization. In addition, they connect geometric algebra and quantum theory, discussing the Dirac equation, wave functions, and fiber bundles. The final chapter focuses on the application of geometric algebra to problems of the quantization of gravity.

By covering the powerful methodology of applying geometric algebra to all branches of physics, this book provides a pioneering text for undergraduate and graduate students as well as a useful reference for researchers in the field.

Harcover, 184 pages, Taylor and Francis, 1st Edition, 2 December 2006.

Clifford algebra in Sir Roger Penrose’s Cycles of Time

by Johannes Koelman of Science 20

Equations don’t sell. Pop science editors tell us that each equation added to a book halves its sales figure. If this is true, Sir Roger Penrose’s Cycles of Time, which was recently released in the US, and which I can testify sold at least one copy, would have sold by the billions if only the editor would have scrapped half of the equations.

With his 2004 book The Road To Reality Penrose has shown to be capable of blurring the distinction between textbooks and pop science writings.Cycles of Time continues in this tradition. I applaud Renrose’s non-populistic attitude, and admire his style. Reading ‘The Road’ and ‘Cycles’ is like listening to talks by Penrose himself. A Penrose who does not shy away from in-depth explanations and who dives deep into the beauty of mathematical physics. Penrose boldly presents spinors, twistors, Clifford algebras and conformal diagrams to the general public. I know of no other pop-science writer who dares to tread into this territory.

Read more at Science 20

Computations with Clifford and Grassmann Algebras

Rafal Ablamowicz,

Department of Mathematics, Tennessee Technological University

Abstract

Various computations in Grassmann and Clifford algebras can be
performed with a Maple package CLIFFORD. It can solve algebraic equations when searching for general elements satisfying certain conditions, solve an eigenvalue problem for a Clifford number, and find its minimal polynomial. It can compute with quaternions, octonions, and matrices with entries in Cl(B)-the Clifford algebra of a vector space V endowed with an arbitrary bilinear form B. It uses standard (undotted) Grassmann basis in Cl(Q) but when the antisymmetric part of B is non zero, it can also compute in a dotted Grassmann basis. Some examples of computations are discussed.

Citation:

Rafal Ablamowicz, Computations with Clifford and Grassmann Algebras, Technical Report, Department of Mathematics, Tennessee Technological University, 2009.  49 pages.

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