  Quantum mechanics can be formulated in terms of phase-space functions,
according to Wigner's approach. A generalization of this approach consists in
replacing the density operators of the standard formulation with suitable
functions, the so-called generalized Wigner functions or (group-covariant)
tomograms, obtained by means of group-theoretical methods. A typical problem
arising in this context is to express the evolution of a quantum system in
terms of tomograms. In the case of a (suitable) open quantum system, the
dynamics can be described by means of a quantum dynamical semigroup 'in
disguise', namely, by a semigroup of operators acting on tomograms rather than
on density operators. We focus on a special class of quantum dynamical
semigroups, the twirling semigroups, that have interesting applications, e.g.,
in quantum information science. The 'disguised counterparts' of the twirling
semigroups, i.e., the corresponding semigroups acting on tomograms, form a
class of semigroups of operators that we call tomographic semigroups. We show
that the twirling semigroups and the tomographic semigroups can be encompassed
in a unique theoretical framework, a class of semigroups of operators including
also the probability semigroups of classical probability theory, so achieving a
deeper insight into both the mathematical and the physical aspects of the
problem.
