Position operators for the relativistic non-interacting n-particle system

The subject under consideration is a system of n non-interacting particles with spin, being described by a tensor product of n unitary irreducible massive representations of the Poincare group. A unitary transformation that effects a separation of centre-of-mass variables and internal variables is constructed. By means of this transformation, for any of the n particles there are constructed two position operators both acting on the internal variables only. The first of these operators (called the internal position) commutes with all spatial translations and with the centre-of-mass position, the second one (called the impact position) commutes moreover with all time translations. It is argued that the impact position may be interpreted as the internal position taken at the instant when the n particles are most closely together. By considering spatial separation properties, it is shown that both the internal position and the impact position of any particle depend essentially on the location of all particles of the system. (author)