The Poincar group in a demisemidirect product with a non-associative algebra with representations that Include particles and quarks
- Department of Mathematics University of Denver and Florida Atlantic University (United States)
The quarks have always been a puzzle, as have the particles' mass and mass/spin relations as they seemed to have no coordinates in configuration space and/or momentum space. The solution to this seems to lie in the marriage of ordinary Poincare group representations with a non-associative algebra made through a demisemidirect product. Then, the work of G. Dixon applies; so, we may obtain all the relations between masses, mass and spin, and the attribution of position and momentum to quarks--this in spite of the old restriction that the Poincare 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 briefly discuss a possible connection between the phase space representations of the Poincare group and the phase space representations of the object we will obtain. This will take us into Leibniz (co)homology.
- OSTI ID:
- 21254866
- Journal Information:
- AIP Conference Proceedings, Vol. 1079, Issue 1; Conference: 27. workshop on geometric methods in physics, Bialowieza (Poland), 29 Jun - 5 Jul 2008; Other Information: DOI: 10.1063/1.3043850; (c) 2008 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
- Country of Publication:
- United States
- Language:
- English
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