In this context, the extended phase space of the particle, including time [x.sup.0] and its conjugate momentum -[p.sub.0], is quantized and canonical coordinates ([p.sub.[mu]], [x.sup.v]) become self- adjoint operators [mathematical expression not reproducible] on a kinematical Hilbert space K satisfying canonical commutation relations:
Noncommutative spacetime coordinates [[??].sup.v] are defined via (23) and the action of deformed relativistic symmetries ([LAMBDA], a) is given by the ordinary Poincaree action on the standard canonical coordinates [mathematical expression not reproducible]:
As for the canonical coordinates, they are given by
For n = 4, the canonical coordinates ([q.sub.1], [q.sub.2], [p.sub.1], [p.sub.2]) are obtained more explicitly from (35) and (36) as
The references mentioned above mainly use canonical coordinates
. The use of isotropic coordinates may provide new insights and possibly lead to new solutions.
(4), the calculation of the canonical momenta [[pi].sub.i] (the canonical coordinates are [[xi].sub.i] = x, y, z) is straightforward
The Cartesian components of the time-derivative of the relativistic momentum can be written in terms of the canonical coordinates and their derivatives, following a differentiation of Eq.