open access

https://hdl.handle.net/2115/59279

On the Logical Origin of the Laws Governing the Fundamental Forces of Nature : A New Axiomatic Matrix Approach

英語

The Fundamental Forces of Nature

2015-01

Archive for Studies in Logic (AFSIL)

16(1)

1-87

https://cds.cern.ch/record/1980381/

The main idea of this article is based on my previous publications (Refs. [1], [2], [3], [4], 1997-1998). In this article we present a new axiomatic matrix approach (and subsequently constructing a linearization theory) based on the ring theory and the generalized Clifford algebra. On the basis of this (primary) mathematical approach and also the assumption of discreteness of the relativistic energy-momentum (D-momentum), by linearization (and simultaneous parameterization, as necessary algebraic conditions), followed by "first" quantization of the relativistic energymomentum relation, a unique and original set of the general relativistic single-particle wave equations are derived directly. These equations are shown to correspond to certain massive forms of the laws governing the fundamental forces of nature, including the Gravitational, Electromagnetic and Nuclear field equations (which based on this approach are solely formulable in (1+3) dimensional space-time), in addition to the (half-integer spin) single-particle wave equations such as the Dirac equation (formulated solely in (1+2) dimensional space-time). Each derived singleparticle field equation is in a complex tensor form, where in matrix representation (i.e. in the geometric algebra formulation) it could be written in the form of two coupled symmetric equations – which assumedly have chiral symmetry if the particle wave equation be source-free. We show that the massless cases of the complex relativistic wave equations so obtained correspond to the classical fields including the Einstein, Maxwell and Yang-Mills field equations. In particular, a unique massive form of the general theory of relativity – with a definite complex torsion – is shown to be obtained solely by first quantization of a special relativistic algebraic matrix relation. Moreover, it is shown that the massive Lagrangian density of the obtained Maxwell and Yang-Mills fields could be also locally gauge invariant – where these fields are formally re-presented on a background space-time with certain (coupled) complex torsion which is generated by the invariant mass of the gauge field carrier particle. Subsequently, in agreement with certain experimental data, the invariant mass of a particle (that would be identified as massive photon) has been specified (m0 ≈ 1.4070696 ×10^-41 kg), which is coupled with background space-time geometry. Assuming our approach is the unique and principal way for deriving (all) the laws governing the fundamental forces of nature, then based on the unique structure of general relativistic single-particle wave equations derived and also the assumption of chiral symmetry as a basic discrete symmetry of the source-free cases of these fields, it is shown that the universe cannot have more than four space-time dimensions. In addition, a mathematical argument for the asymmetry of left and right handed (interacting) particles is presented. Furthermore, on the basis of definite mathematical structure of the field equations derived, we also conclude that magnetic monopoles (in contrast with electric monopoles) could not exist in nature.

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