Some Physics Questions in Hyperbolic Complex Space

Abstract

In hyperbolic complex space, the Clifford algebra is isomorphic to that of a corresponding Minkowski geometry. We define the hyperbolic imaginary unit j (j2 = 1, j ≠ ± 1, j* = − j) to generate a class of Clifford algebras. We can introduce a class of non-Euclidean spaces and discuss the general form of 4-dimensional Lorentz transformation, and related special relativistic physics.