Clifford algebra and the projective model of Minkowski (pseudo-Euclidean) spaces

Abstract

I apply the algebraic framework introduced in arXiv:1101.4542v3[math.MG] to Minkowski (pseudo-Euclidean) spaces in 2, 3, and 4 dimensions. The exposition follows the template established in arXiv:1307.2917[math.MG] for Euclidean spaces. The emphasis is on geometric structures, but some contact with special relativity is made by considering relativistic addition of velocities and Lorentz transformations, both of which can be seen as rotation applied to points and to lines. The language used in the paper reflects the emphasis on geometry, rather than applications to special relativity. The use of Clifford algebra greatly simplifies the study of Minkowski spaces, since unintuitive synthetic techniques are replaced by algebraic calculations.