  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.
