  The canonical decomposition of a real Klein-Gordon field in collective and
relative variables proposed by Longhi and Materassi is reformulated on
spacelike hypersurfaces. This allows to obtain the complete canonical reduction
of the system on Wigner hyperplanes, namely in the rest-frame Wigner-covariant
instant form of dynamics. From the study of Dixon's multipoles for the
energy-momentum tensor on the Wigner hyperplanes we derive the definition of
the canonical center-of-mass variable for a Klein-Gordon field configuration:
it turns out that the Longhi-Materassi global variable should be interpreted as
a center of phase of the field configuration. A detailed study of the
kinematical "external" and "internal" properties of the field configuration on
the Wigner hyperplanes is done. The construction is then extended to charged
Klein-Gordon fields: the centers of phase of the two real components can be
combined to define a global center of phase and a collective relative variable
describing the action-reaction between the two Feshbach-Villars components of
the field with definite sign of energy and charge. The Dixon multipoles for
both the energy-momentum and the electromagnetic current are given. Also the
coupling of the Klein-Gordon field to scalar relativistic particles is studied
and it is shown that in the reduced phase space, besides the particle and field
relative variables, there is also a collective relative variable describing the
relative motion of the particle subsytem with respect to the field one.
