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, including 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 discuss the Dirac equation, wave functions, fiber bundles, and 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.
- Introduces the mathematical fundamentals of geometric algebra, including bivectors, multivectors, and spinor theory
- Provides examples of geometric algebra applications to the polarization of electromagnetic waves, neutron interferometry in gravitational fields, fiber bundles, and quantum theory
- Includes helpful information on complex numbers in geometric algebra formulations of electrodynamics and on plane-wave solutions to Maxwell’s equations
- Explores the basic aspects of intrinsic spin and charge conjugation
Venzo de Sabbata is a professor at the Universities of Bologna and Ferrara, Italy, and Bidyut Kumar Datta teaches at the M.P. Birla Institute of Fundamental Research, Calcutta, India. Their research interests include general relativity and quantum gravity.
1. The Basis for Geometric Algebra
3. Euclidean Plane
4. The Pseudoscalar and Imaginary Unit
5. Real Dirac Algebra
6. Spinor and Quaternion Algebra
7. Maxwell Equations
8. Electromagnetic Field in Space and Time (Polarization of Electromagnetic Waves)
9. General Observations and Generators of Rotations (Neutron Interferometer Experiment)
10. Quantum Gravity in Real Space-Time (Commutators and Anticommutators)
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