Matrix Representation of Special Relativity

Abstract

I compare the matrix representation of the basic statements of Special Relativity with the conventional vector space representation. It is shown, that the matrix form reproduces all equations in a very concise and elegant form, namely: Maxwell equations, Lorentz-force, energy-momentum tensor, Dirac-equation and Lagrangians. The main thesis is, however, that both forms are nevertheless not equivalent, but matrix representation is superior and gives a deeper insight into physical reality, because it is based on much less assumptions. It allows a better understanding of Minkowski spacetime on the basis of matrix algebra. An escpecially remarkable result of the consequent usage of this alge- braic concept is the formulation of Diracs equation in a novel matrix form. This equation can be generalized to include a new variant of Yang-Mills gauge fields, which possibly express unified electro-weak interactions in a new way.