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

Abstract: In this article, as a new mathematical approach to origin of the basic laws of nature, using a new algebra-axiomatic matrix formalism based on the ring theory and Clifford algebras , "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 (& completely) from only a very few axioms"; where in agreement with the rational Lorentz group, it is also basically assumed that the components of relativistic energy-momentum can only take rational values. Based on the definite mathematical formalism of this axiomatic approach, along with the C, P and T symmetries (represented by the corresponding quantum matrix operators) of the fundamentally derived field equations, it is concluded that the universe could be realized solely with the (1+2) and (1+3)-dimensional space-times. Moreover, it is shown that the (1+3)-dimensional cases of derived two classes of field equations, represent respectively new massive forms of bispinor fields of spin-2, and spin-1 particles; and (1+2)-dimensional cases of these equations represent (asymptotically) new massive forms of bispinor fields of spin-3/2 and spin-1/2 particles, respectively. On this basis, following certain forms of the gauge symmetries of these derived fields, along with the known elementary particles, eight new elementary particles including a spin-3/2 fermion, two chargeless leptons, two chargeless quarks, and three spin-1 (massive) bosons are predicted uniquely by this axiomatic matrix approach. As a particular result, based on the definite formulation of derived field equations, it has also been concluded that magnetic monopoles cannot exist in nature.