Geometric Algebra and Applications to Physics

Venzo de Sabbata, Bidyut Kumar Datta

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English

CRC Press
19 September 2019

Applied mathematics; Mathematical physics

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.

By: Venzo de Sabbata, Bidyut Kumar Datta
Imprint: CRC Press
Country of Publication: United Kingdom
Dimensions: Height: 234mm, Width: 156mm,
Weight: 263g
ISBN: 9780367389789
ISBN 10: 0367389789
Pages: 184
Publication Date: 19 September 2019
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

The Basis for Geometric Algebra. Multivectors. Euclidean Plane. The Pseudoscalar and Imaginary Unit. Real Dirac Algebra. Spinor and Quaternion Algebra. Maxwell Equations. Electromagnetic Field in Space and Time (Polarization of Electromagnetic Waves). General Observations and Generators of Rotations (Neutron Interferometer Experiment). Quantum Gravity in Real Space-Time (Commutators and Anticommutators).

de Sabbata, Venzo; Datta, Bidyut Kumar