Geometric Algebra and Applications to Physics

Book Details

• Author: Bidyut Kumar Datta

• Brand: CRC Press

• Edition: 1st Edition

• Binding: Paperback

• Number of Pages: 184

• Release Date: 27-09-2019

• ISBN: 9780367389789

• Package Dimensions: 9.3 x 6.1 x 0.4 inches

• Languages: English

About the Book

Geometric Algebra and Applications to Physics offers an introduction to geometric algebra as a key discipline within mathematical physics. This book not only presents the fundamentals of geometric algebra but also demonstrates its broad applicability to various problems in physics, particularly in experimental settings.

The text is structured into two main parts:

1. Mathematical Foundations: The first few chapters establish the essential concepts of geometric algebra. Topics covered include:

   • Postulates and the underlying framework of geometric algebra

   • Bivectors, multivectors, and their operators

   • Spinor and Lorentz rotations

   • Clifford algebra and its generalizations, including applications in three-dimensional space

2. Physical Applications: The subsequent chapters focus on practical applications of geometric algebra, including:

   • Rewriting Maxwell's equations using space-time algebra

   • Understanding the polarization states of electromagnetic waves

   • Connecting geometric algebra with quantum theory, including the Dirac equation, wave functions, and fiber bundles

   • Analyzing problems related to the quantization of gravity

This book serves as an essential reference for undergraduate and graduate students, as well as researchers interested in the advanced application of geometric algebra in physics.

Review

This pioneering text provides an accessible yet comprehensive guide to the powerful methodology of geometric algebra, making it an invaluable resource for anyone looking to explore its diverse applications in physics.