On the structure of space-time and linear evolution equations

摘要

Let {T υ : υ ∈ [0,c)} the one-parameter semi-module of Lorentz op-erators on R 4 with infinitesimal generator T , where c is the constantspeed of light in vacuum. In this paper the space-time of special theoryof relativity is considered as affine and ordered vector space. We studythe topology of space-time and we consider the velocity differential evo-lution equationA ￠ y(υ) = f(υ) where f : [0,c) → R 4 is a givenfunction and the corresponding linear time differential evolution equa-tion, where A is the corresponding matrix of the infinitesimal generatorT.