A Logical Derivation of the Laws Governing the Fundamental Forces of Nature: A New Axiomatic-Algebraic (Matrix) Approach

In this article I present a new axiomatic algebraic (matrix) approach based on the ring theory (including the integral domain) and the generalized Clifford algebras. On the basis of this (primary) mathematical approach, by linearization (and simultaneous parameterization, as necessary algebraic conditions), followed by first quantization of the relativistic energy-momentum relation (defined algebraically for a single particle with invariant mass m_0), a unique and original set of the general relativistic (single-particle) wave equations are derived directly. These equations are shown to correspond uniquely to certain massive forms of the laws governing the fundamental forces of nature, including the Gravitational (Einstein), Electromagnetic (Maxwell) and Nuclear (Yang-Mills) field equations (formulated solely in (1+3) dimensional space-time), in addition to the (half-integer spin) single-particle wave equations such as the Dirac equation (which are formulated solely in (1+2) dimensional space-time). In particular, a unique massive form of the general theory of relativity - with a definite complex torsion - is shown to be obtained solely by first quantization of a special relativistic algebraic matrix relation. In addition, it is shown that the "massive " Lagrangian density of the obtained Maxwell and Yang- Mills fields could be also locally gauge invariant - where these fields are formally re-presented on a background space-time with certain complex torsion which generates the mass of gauge field carrier particles (and vice versa). Subsequently, in agreement with certain experimental data, the invariant mass of a particle (that actually would be identified as massive photon) has been specified (m_γ ≈ 1.470696 ×10^-41 kg), which is coupled to background space-time geometry. Moreover, based on the unique structure of general relativistic particle wave equations derived and also the assumption of chiral symmetry as a basic discrete symmetry of the source-free cases of these fields, it has been proven that the universe cannot have more than four space-time dimensions. In addition, an argument for the asymmetry of left and right handed (interacting) particles is presented. Furthermore, on the basis of definite mathematical structure of the field equations derived, it is also shown that magnetic monopoles (in contrast with electric monopoles) could not exist in nature. Comments: 97 Pages. A summary of a submitted and accepted research project, Ramin Zahedi, (On "Foundations of Physics"), Japan, 2014 - 2015; (Expanded version). Invited and Presented article at: The 4th International Conference on New Frontiers in Physics ICNFP2015, Europe (CERN), (https://indico.cern.ch/e/icnfp2015); The 2016 SIAM International Conference on Mathematical Aspects of Materials Science, Philadelphia, USA, (https://www.siam.org/meetings/ms16/); The 17th International Conference on Quantum Foundations: Quantum and Beyond, International Centre for Mathematical Modeling in Physics, Engineering and Cognitive Sciences ( ICMM), Linnaeus University, Sweden, 2016, (https://lnu.se/en/qb/); The 2016 International Conference on Algebraic Geometry and Mathematical Physics (AGMP 2016), University of Tromsø, Norway, (https://site.uit.no/); International Conference on Noncommutative Geometry, Quantum Symmetries and Quantum Gravity (II), XXXVII Max Born International Symposium, Wroclaw University, Poland, 2016, (http://ift.uni.wroc.pl/~mborn37/); The 21st International Conference on General Relativity and Gravitation, Columbia University, New York, USA, (https://www.columbia.edu/ , http://www.gr21.org/) . Keywords (Part I): Ontology, Physical Reality, Digital Philosophy, Universe as a Computational Simulation; (Part II): Foundations of Mathematics, Ontology, Fundamental physics, Basic Quantized (Discrete) Quantities of Physics, Mathematical Foundation of the General Theory of Relativity, Ring Theory, Generalized Clifford Algebras, Quantum Operators, General Relativistic (single-particle) Wave Equations, Laws Governing the Fundamental Forces of Nature, Chiral Symmetry and the Number of Space-Time Dimensions. Acknowledgements: Special thanks are extended to Prof. and Academician Vitaly L. Ginzburg (Russia), Prof. and Academician Dmitry V. Shirkov (Russia), Prof. Leonid A . Shelepin (Russia), Prof. Vladimir Ya. Fainberg (Russia), Prof. Wolfgang Rindler (USA), Prof. Roman W. Jackiw (USA), Prof. Roger Penrose (UK), Prof. Steven Weinberg (USA), Prof. Ezra T. Newman (USA), Prof. Graham Jameson (UK), Prof. Sergey A. Reshetnjak (Russia), Prof. Sir Michael Atiyah (UK) (who, in particular, kindly encouraged me to continue this work as a new unorthodox (primary) mathematical approach to fundamental physics), and many others for their support and valuable guidance during my studies and research. EXTERNAL URLs (UPDATED VERSION): https://indico.cern.ch/event/344173/session/22/contribution/422/attachments/1140145/1646101/R.a.Zahedi--OnDiscretePhysics-Jan.2015-signed.pdf , https://cds.cern.ch/record/1980381/ , https://INSPIREHEP.net/record/1387680/ , http://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/59279/3/R.A.Zahedi--Forces.of.Nature.Laws-Jan.2015-signed.pdf