Abstract
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.
Highlights
Introduction and SummaryWhy do the fundamental forces of nature manifest in the way, shape, and form that they do? This is one of the greatest ontological questions that science can investigate
As a new mathematical approach to origin of the laws of nature, using a new basic algebraic axiomatic 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, are derived uniquely from only a very few axioms”and, in agreement with the rational Lorentz group, it is basically assumed that the components of relativistic energy-momentum can only take rational values
Concerning the basic assumption of the rationality of relativistic energy-momentum, it is necessary to note that the rational Lorentz symmetry group is dense in the general form of Lorentz group, and is compatible with the necessary conditions required basically for the formalism of a consistent relativistic quantum theory [15]
Summary
Why do the fundamental forces of nature (i.e., the forces that appear to cause all the movements and interactions in the universe) manifest in the way, shape, and form that they do? This is one of the greatest ontological questions that science can investigate. We have shown that by an initial quantization (followed by a basic procedure of minimal coupling to space-time geometry) of these determined systems of linear equations, a unique set of two definite classes of general covariant massive (tensor) field equations (with matrix formalisms compatible with certain Clifford, and Weyl algebras) is derived, corresponding with various space-time dimensions, respectively.
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