This text takes an emerging approach to physics, emphasizing important geometrical structures that lay the foundations of much of modern theory. The subject of Clifford algebras is presented in efficient geometric language - common concepts in physics are clarified, united and extended. The text serves as a pedgogical tool for either self-study or in undergraduate/graduate courses. Topics covered include: history of teaching algebras; linear algebra; gravity; spinors; applications in engineering; spacetime algebra and line geometry; and Clifford algebra with Maple.
1 Introduction.- 2 Clifford Algebras and Spinor Operators.- 3 Introduction to Geometric Algebras.- 4 Linear Transformations.- 5 Directed Integration.- 6 Linear Algebra.- 7 Dynamics.- 8 Electromagnetism.- 9 Electron Physics I.- 10 Electron Physics II.- 11 STA and the Interpretation of Quantum Mechanics.- 12 Gravity I — Introduction.- 13 Gravity II — Field Equations.- 14 Gravity III — First Applications.- 15 Gravity IV — The ‘Intrinsic’ Method.- 16 Gravity V — Further Applications.- 17 The Paravector Model of Spacetime.- 18 Eigenspinors in Electrodynamics.- 19 Eigenspinors in Quantum Theory.- 20 Eigenspinors in Curved Spacetime.- 21 Spinors: Lorentz Group.- 22 Spinors: Clifford Algebra.- 23 Genersd Relativity: An Overview.- 24 Spinors in General Relativity.- 25 Hypergravity I.- 26 Hypergravity II.- 27 Properties of Clifford Algebras for Fundamental Particles.- 28 The Extended Grassmann Algebra of R3.- 29 Geometric Algebra: Applications in Engineering.- 30 Projective Quadrics, Poles, Polars, and Legendre Transformations.- 31 Spacetime Algebra and Line Geometry.- 32 Generalizations of Clifford Algebra.- 33 Clifford Algebra Computations with Maple.
"Of interest due to the many provocative physical interpretations of quantum mechanics and gravitational theory suggested by the Clifford algebra approach to these theories." -Mathematical Reviews
