Relativistic Position Operator for Free Particles

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Abstract
Certain definitions and derivations for the relativistic center of mass are considered and are related to the position operator corresponding to the representation proposed in a previous paper. It is shown that the classical definition of Pryce has indeed a more direct correspondence with our representation than the Foldy‐Wouthuysen representation, in spite of the fact that Pryce's particular method of symmetrization leads to the latter. In the process of derivation, the points of view of Synge, Pryce, and Shirokov are compared and the expressions for the velocity and the intrinsic angular momentum corresponding to the different definitions are given. In the Appendix, our operator is compared with that of Newton and Wigner for the case of spin ½.

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