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

TL;DR

This paper introduces a novel algebraic-axiomatic matrix formalism to derive fundamental physical laws, predicting new particles and asserting the non-existence of magnetic monopoles, all from minimal axioms and symmetry considerations.

Contribution

It presents a new mathematical framework based on ring theory and Clifford algebras that uniquely derives fundamental laws and predicts new elementary particles.

Findings

Derivation of fundamental laws from few axioms

Prediction of eight new elementary particles

Conclusion that magnetic monopoles cannot exist

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.