  Several recent studies have concerned the faith of classical symmetries in
quantum space-time. In particular, it appears likely that quantum (discretized,
noncommutative,...) versions of Minkowski space-time would not enjoy the
classical Lorentz symmetries. I compare two interesting cases: the case in
which the classical symmetries are "broken", i.e. at the quantum level some
classical symmetries are lost, and the case in which the classical symmetries
are "deformed", i.e. the quantum space-time has as many symmetries as its
classical counterpart but the nature of these symmetries is affected by the
space-time quantization procedure. While some general features, such as the
emergence of deformed dispersion relations, characterize both the
symmetry-breaking case and the symmetry-deformation case, the two scenarios are
also characterized by sharp differences, even concerning the nature of the new
effects predicted. I illustrate this point within an illustrative calculation
concerning the role of space-time symmetries in the evaluation of
particle-decay amplitudes. The results of the analysis here reported also show
that the indications obtained by certain dimensional arguments, such as the
ones recently considered in hep-ph/0106309 may fail to uncover some key
features of quantum space-time symmetries.
