  According to the Hamiltonian formalism, nonrelativistic phase space may be
considered as an arena of physics, with momentum and position treated as
independent variables. Invariance of x^2+p^2 constitutes then a natural
generalization of ordinary rotational invariance. We consider Dirac-like
linearization of this form, with position and momentum satisfying standard
commutation relations. This leads to the identification of a quantum-level
structure from which some phase space properties might emerge. Genuine
rotations and reflections in phase space are tied to the existence of new
quantum numbers, unrelated to ordinary 3D space. Their properties allow their
identification with the internal quantum numbers characterising the structure
of a single quark-lepton generation in the Standard Model. In particular, the
algebraic structure of the Harari-Shupe preon model of fundamental particles is
reproduced exactly and without invoking any subparticles. Analysis of the
Clifford algebra of nonrelativistic phase space singles out an element which
might be associated with the concept of lepton mass. This element is
transformed into a corresponding element for a single coloured quark, leading
to a generalization of the concept of mass and a different starting point for
the discussion of quark unobservability.
