Could the Fundamental Laws of Nature be Inferred Mathematically from Only Few Axioms?

Abstract

The answer is "Yes". As it has been shown in the Ref.[1] (22 Sep.2017, see also the comments), useing a new definite mathematical axiomatic-algebraic matrix approach, all the fundamental laws of nature could be derived uniquely (where the axiom of "no zero divisors" of the ring of integers has been generilzed and written in a new definite formulation, then basically assuming that all the physical quantities could only and only take the rational values). Based on this new mathematical approach along with the C, P and T symmetries of the derived field equations, it is concluded that the universe could be realized solely with the (2+1) and (3+1)-dimensional space-times. Moreover it is shown that the (3+1) dimensional cases of the directly determinated general covariant field equations (including two definite classes: a two indexes and a four indexes tensor fields), respectively, represent two new massive forms of the bispinor fields of spin-1and spin-2 particles; and the (2+1)-dimensional cases of the drived equations (including: a two indexes and a four indexes tensor fields), represent (asymptotically) two new massive forms of the bispinor fields of spin-3/2 and spin-1/2 particles, respectively. As a particular result, based on the formulation of the derived Electromagnetic Maxwell equations (representing by the bispinor fields of spin-1 particles, including new field equations - corresponding to the YangMills equations - compatible with two specified forms of the gauge symmetry groups), it has been concluded that magnetic monopoles could not exist in the nature to any extend. Furthermore, as the only elementary particles that could be existed in nature, along with the all discovered particles, eight new particles, including four charge-less right-handed spin-1/2 fermions (two leptons and two quarks), and a spin-3/2 fermion, and also three spin-1 massive bosons are also solely predicted.