From quantum field theory to quantum mechanics

We construct the algebra of operators acting on Hilbert spaces Quantum Mechanics for systems $N$ identical particles from field in Fock space Field Theory by providing explicit relation between position and momentum former latter. This is done context non-interacting Klein-Gordon field. It may not be possible to extend procedure interacting theories since it relies crucially particle number conservation. find nevertheless important that such an can found at least free fields. also comes out whatever statistics obey (either commuting or anticommuting), commutation relations. The construction raises issue localizability Relativistic Mechanics, as operator a single turns Newton-Wigner operator. make some clarifications interpretation localized states we consider transformation properties under Lorentz transformations, showing they do transform tensors, rather manner preserves canonical