2007/01/09 by Wolfgang Koehler, Koehler, Wolfgang
Physics and Astronomy · #FOS: Physical sciences #General Physics (physics.gen-ph) #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #Relativity and Gravitational Theory #physics.gen-ph
paper · pdf · doi:10.48550/arxiv.physics/0701105
vers. 3, 11 pages, comments on neutrinos added, partially revised
openalex publication_date 2007/01/09 · arxiv created 2007/03/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.