A canonical decomposition in collective and relative variables of a Klein-Gordon field in the rest-frame Wigner-covariant instant form

The canonical decomposition of a real Klein-Gordon field in collective and relative variables proposed by Longhi and Materassi is reformulated on spac elike hypersurfaces. This allows us to obtain the complete canonical reduct ion of the system on Wigner hyperplanes, namely in the rest-frame Wigner-co variant instant form of dynamics. From the study of Dixon's multipoles for the energy-momentum tensor on the Wigner hyperplanes we derive the definiti on of the canonical center-of-mass variable for a Klein-Gordon field config uration: it turns out that the Longhi-Materassi global variable should be i nterpreted as a center of phase of the field configuration. A detailed stud y of the kinematical "external" and "internal" properties of the field conf iguration on the Wigner hyperplanes is done. The construction is then exten ded to charged Klein-Gordon fields: the centers of phase of the two real co mponents can be combined to define a global center of phase and a collectiv e relative variable describing the action-reaction between the two Feshbach -Villars components of the field with definite sign of energy and charge. T he Dixon multipoles for both the energy-momentum and the electromagnetic cu rrent are given. Also the coupling of the Klein-Gordon field to scalar rela tivistic particles is studied and it is shown that in the reduced phase spa ce, besides the particle and field relative variables, there is also a coll ective relative variable describing the relative motion of the particle sub system with respect to the field one.