Quaternionic formulation of tachyons, superluminal transformations and a complex space-time

A theory of tachyons and superluminal transformations is developed on the basis of the quaternionic formulation. We have introduced a complex space-time and a complex transformation group which contains both Lorentz transformations and superluminal transformations. The complex space-time «the biquaternion space» which is closed under the superluminal transformations is introduced. The principle of special relativity, such as the conservation of the quadratic form of the metric of the space-time, and the principle of duality are extended to the complex space-time and to bradyons, luxons and tachyons under the complex transformations. Several characteristic features of the superluminal transformations and of tachyons are derived.