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A Unique Mathematical Derivation of the Fundamental Laws of Nature Based on a New Algebraic-Axiomatic (Matrix) Approach

Logic and Philosophy of Science Research Group, Hokkaido University, Hokkaido 060-0808, Japan
Invited and presented article at The 21st International Conference on General Relativity and Gravitation, Columbia University, New York, NY, USA, 2016. ‡ This work has been done and published during my research fellowship, 2007–2016.
Universe 2017, 3(4), 67; https://doi.org/10.3390/universe3040067
Received: 10 July 2017 / Revised: 25 August 2017 / Accepted: 28 August 2017 / Published: 22 September 2017
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. View Full-Text
Keywords: mathematical origin of the fundamental laws of nature; gauge-group theoretic prediction of eight new elementary particles; CPT symmetry as the only combination of C, P and T symmetries definable for the interacting fields; realization of the universe solely with (1 + 2) and (1 + 3)-dimensional space-times; a basic mathematical proof for the absence of monopoles in nature; Space-time torsion as origin of particles’ mass; Spin-1/2, 3/2, 1, 2 elementary particles as the only existing particles in nature mathematical origin of the fundamental laws of nature; gauge-group theoretic prediction of eight new elementary particles; CPT symmetry as the only combination of C, P and T symmetries definable for the interacting fields; realization of the universe solely with (1 + 2) and (1 + 3)-dimensional space-times; a basic mathematical proof for the absence of monopoles in nature; Space-time torsion as origin of particles’ mass; Spin-1/2, 3/2, 1, 2 elementary particles as the only existing particles in nature
MDPI and ACS Style

Zahedi, R. A Unique Mathematical Derivation of the Fundamental Laws of Nature Based on a New Algebraic-Axiomatic (Matrix) Approach. Universe 2017, 3, 67.

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