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.Comment: 10 pages, presented at a Conference in Honor of Murray Gell-Mann's
80th Birthday, 24-26 February, 2010, Nanyang Technical University, Sigapor
