canonical coordinates


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canonical coordinates

[kə′nän·ə·kəl kō′ȯrd·ən·əts]
(mathematics)
Any set of generalized coordinates of a system together with their conjugate momenta.
References in periodicals archive ?
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.