Clifford (Geometric) Algebras: With Applications to Physics, Mathematics, and Engineering

Abstract

History of Clifford algebras teaching Clifford algebras operator approach to spinors flags, poles and dipoles introduction to geometric algebras linear transformations directed integration linear algebra dynamics electromagnetism electro physics I,II STA and the interpretation of quantum mechanics gravity I - introduction gravity II - field equations gravity III - first applications gravity IV - the intrinsic method gravity V - further applications the paravector model of spacetime Eigenspinors in electrodynamics Eigenspinors in quantum theory Eigenspinors in curved spacetime spinors - Lorentz group spinors - Clifford algebra general relativity - an overview spinors in general relativity hypergravity I,II properties of Clifford algebras for fundamental particles extended Grassmann algebra of R3 applications in engineering - computer vision and robotics projective quadrics, poles, polars and Legendre transformation spacetime algebra and line geometry generalizations of Clifford algebras Clifford algebra computations with Maple.