2015/01/31 by Ramin Zahedi
Mathematics · Physics and Astronomy · Social Sciences · #Algebra over a field #Algebraic and Geometric Analysis #Axiom #Covariant transformation #International Science and Diplomacy #Invariant (physics) #Linearization #Lorentz covariance #Lorentz transformation #Quantum and Classical Electrodynamics #Rotation formalisms in three dimensions #Spinor #physics.gen-ph
paper · pdf · doi:10.3390/universe3040067
published in Universe 3(4), 67 (Multidisciplinary Digital Publishing Institute) · 83 Pages. Presented article at "The 21st International Conference on General Relativity and Gravitation, Columbia University, New York, USA, 2016". CERN Document-Record: 1980381, 2015. https://www.mdpi.com/2218-1997/3/4/67/
openalex created_date 2017/09/15 · openalex publication_date 2017/09/22 · arxiv created 2019/10/15 · arxiv updated 2019/10/16 · openalex updated_date 2026/08/05
In this article, as a new mathematical approach to origin of the laws of nature, using a new basic algebraic axiomatic (matrix) formalism based on the ring theory and Clifford algebras (presented in Section 2), “it is shown that certain mathematical forms of fundamental laws of nature, including laws governing the fundamental forces of nature (represented by a set of two definite classes of general covariant massive field equations, with new matrix formalisms), are derived uniquely from only a very few axioms.” In agreement with the rational Lorentz group, it is also basically assumed that the components of relativistic energy-momentum can only take rational values. In essence, the main scheme of this new mathematical axiomatic approach to the fundamental laws of nature is as follows: First, based on the assumption of the rationality of D-momentum and by linearization (along with a parameterization procedure) of the Lorentz invariant energy-momentum quadratic relation, a unique set of Lorentz invariant systems of homogeneous linear equations (with matrix formalisms compatible with certain Clifford and symmetric algebras) is derived. Then by an initial quantization (followed by a basic procedure of minimal coupling to space-time geometry) of these determined systems of linear equations, a set of two classes of general covariant massive (tensor) field equations (with matrix formalisms compatible with certain Clifford, and Weyl algebras) is derived uniquely as well.