Covariant Position Operators, Spin, and Locality

A manifestly covariant formalism is developed suitable for a discussion of position operators for relativistic systems. It is shown that the rest-frame center of mass and the frame-dependent center of mass, which were studied previously by Pryce and M{}ller, and the local Newton-Wigner operator all transform like the spatial part of a four-vector when appropriately interpreted. The formalism allows an equivalent treatment of the space and time components of a position four-vector operator, and manifestly covariant canonical commutation rules are obtained for the three operators mentioned above. Finally it is suggested that the Newton-Wigner operator be interpreted as a center of spin.