Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-06-11
Int.J.Mod.Phys.A25:4889-4899,2010
Physics
High Energy Physics
High Energy Physics - Theory
10 pages, presented at a Conference in Honor of Murray Gell-Mann's 80th Birthday, 24-26 February, 2010, Nanyang Technical Univ
Scientific paper
10.1142/S0217751X10050810
Relativistic dynamics with energy and momentum resricted to an anti-de-Sitter space is presented, specifically in the introduction of coordiate operators conjugate to such momenta. Definition of functions of these operators, their differentiation and integration, all necessary for the development of dynamics is presented. The resulting algebra differs from the standard Heisenberg one, notably in that the space-time coordinates do not commute among each other. The resulting time variable is discrete and the limit to continuous time presents difficulties. A parallel approach, in which an overlap function, between position and momentum states, is obtained from solutions of wave equations on this curved space are also investigated. This approach, likewise, has problems in the that high energy behavior of these overlap functions precludes a space-time definition of action functionals.
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