  In previous work [Rosenbaum M. et al., J. Phys. A: Math. Theor. 40 (2007),
10367-10382, hep-th/0611160] we have shown how for canonical parametrized field
theories, where space-time is placed on the same footing as the other fields in
the theory, the representation of space-time diffeomorphisms provides a very
convenient scheme for analyzing the induced twisted deformation of these
diffeomorphisms, as a result of the space-time noncommutativity. However, for
gauge field theories (and of course also for canonical geometrodynamics) where
the Poisson brackets of the constraints explicitely depend on the embedding
variables, this Poisson algebra cannot be connected directly with a
representation of the complete Lie algebra of space-time diffeomorphisms,
because not all the field variables turn out to have a dynamical character
[Isham C.J., Kuchar K.V., Ann. Physics 164 (1985), 288-315, 316-333].
Nonetheless, such an homomorphic mapping can be recuperated by first modifying
the original action and then adding additional constraints in the formalism in
order to retrieve the original theory, as shown by Kuchar and Stone for the
case of the parametrized Maxwell field in [Kuchar K.V., Stone S.L., Classical
Quantum Gravity 4 (1987), 319-328]. Making use of a combination of all of these
ideas, we are therefore able to apply our canonical reparametrization approach
in order to derive the deformed Lie algebra of the noncommutative space-time
diffeomorphisms as well as to consider how gauge transformations act on the
twisted algebras of gauge and particle fields. Thus, hopefully, adding
clarification on some outstanding issues in the literature concerning the
symmetries for gauge theories in noncommutative space-times.
