Abstract
The quarks and particles’ mass and mass/spin relations are provided with coordinates in configuration space and/or momentum space by means of the marriage of ordinary Poincaré group representations with a non-associative algebra made through a demisemidirect product, in the notation of Leibniz algebras. Thus, we circumvent the restriction that the Poincaré group cannot be extended to a larger group by any means (including the (semi)direct product) to get even the mass relations. Finally, we will discuss a connection between the phase space representations of the Poincaré group and the phase space representations of the associated Leibniz algebra.
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Schroeck, F.E. The Poincaré Group in a Demisemidirect Product with a Non-associative Algebra with Representations that Include Particles and Quarks—II. Int J Theor Phys 48, 3586 (2009). https://doi.org/10.1007/s10773-009-0165-0
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DOI: https://doi.org/10.1007/s10773-009-0165-0