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University of Windsor
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|Welcome to the website for my research on Clifford's Geometric Algebra of Physical Space (APS). The intention is to explain the use of paravectors in the algebra to model spacetime. For other information on my research, please see my webpage under Faculty Overview at www.uwindsor.ca/units/physics/PhysicsM.nsf|
Paravectors are sums of scalars and vectors. If the vector space is 3-dimensional physical space with a Euclidean metric, the paravectors form a linear space of four dimensions with the Minkowski spacetime metric. They provide a covariant formulation of relativity that avoids matrix and tensor components but brings powerful tools such as spinors and projectors.
APS allows an introduction to relativity, suitable for beginning physics students, that avoids the mathematical formalisms of matrices and tensors. It lets students concentrate on the fascinating geometry of spacetime without getting lost in the math. With a minimal subset of the full algebra, students can perform quantitative Lorentz transformations (boosts and rotations) (also available as http://arXiv.org/physics/0406158)
To gain a working knowledge of geometric algebra and an introduction to APS, work through the attached workbook. You will need Adobe Acrobat Reader to view the file: (421 kB).
Here's a somewhat more detailed lecture on Applications of Clifford's Geometric Algebra in Physics: (604 kB)
An application of APS to the motion of charges in electromagnetic waves, with and without axial electric or magnetic fields, is given in this 1999 Phys. Rev aritcle:, and an application to understanding electromagnetic radiation is given in this preprint (new version June 21, 2003):.
A paper with Garret Sobczyk compares relative and absolute formulations of special relativity in APS and STA. See arXiv.org/math-ph/0405026
Two recent papers that use paravectors in APS: Geometry of Paravector Space, with Applications to Relativistic Physics: and Quantum/Classical Interface: an Approach from the Classical Side:
An application of multiple APS to quantum computation:
Bill Baylis email@example.com