dorsal/arxiv
View SchemaElementary Particles as Solutions of a 4-Dimensional Source Equation
| Authors | Jose B. Almeida |
|---|---|
| Categories | |
| ArXiv ID | physics/0303034 |
| URL | https://arxiv.org/abs/physics/0303034 |
Abstract
The author discusses particular solutions of a second order equation designated by source equation. This equation is special because the metric of the space where it is written is influenced by the solution, rendering the equation recursive. The recursion mechanism is established via a first order equation which bears some resemblance to Dirac equation. In this paper the author limits the discussion to solutions with constant norm but makes use of 4-dimensional hypercomplex numbers in matrix representation, a concept that is formally introduced in a section devoted to that aspect. The particular solutions that are found exhibit symmetries that can be assigned to spin, electric and color charges of elementary particles, leaving mass as a free parameter. Massless particles can also be assigned to special solutions of the source equation, with the cases of photons, gluons and gravitons clearly identified, together with another massless particle which does not seem to be related to anything detected experimentally. Another section deals with particle dynamics under fields, showing that both gravitational and electrodynamics can be modelled by geodesics of the spaces whose metric tensors result from the recursion mechanism. Finally the author suggests two lines of future work, one deriving fields from densities and currents of masses and charges and the other one aimed at determining particles' masses.
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"abstract": "The author discusses particular solutions of a second order equation\ndesignated by source equation. This equation is special because the metric of\nthe space where it is written is influenced by the solution, rendering the\nequation recursive. The recursion mechanism is established via a first order\nequation which bears some resemblance to Dirac equation. In this paper the\nauthor limits the discussion to solutions with constant norm but makes use of\n4-dimensional hypercomplex numbers in matrix representation, a concept that is\nformally introduced in a section devoted to that aspect. The particular\nsolutions that are found exhibit symmetries that can be assigned to spin,\nelectric and color charges of elementary particles, leaving mass as a free\nparameter. Massless particles can also be assigned to special solutions of the\nsource equation, with the cases of photons, gluons and gravitons clearly\nidentified, together with another massless particle which does not seem to be\nrelated to anything detected experimentally. Another section deals with\nparticle dynamics under fields, showing that both gravitational and\nelectrodynamics can be modelled by geodesics of the spaces whose metric tensors\nresult from the recursion mechanism. Finally the author suggests two lines of\nfuture work, one deriving fields from densities and currents of masses and\ncharges and the other one aimed at determining particles\u0027 masses.",
"arxiv_id": "physics/0303034",
"authors": [
"Jose B. Almeida"
],
"categories": [
"physics.gen-ph"
],
"title": "Elementary Particles as Solutions of a 4-Dimensional Source Equation",
"url": "https://arxiv.org/abs/physics/0303034"
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