Definitions of the off-shell relative momentum in relativistic theories

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Abstract
A variety of definitions of the relative momentum in off-shell systems are discussed and a set of basic requirements for these momenta are established. The off-mass-shell Wightman-Gårding four-momentum, which has been employed most recently by Morioka and Afnan, is shown to be ambiguously defined, and it is shown that the relative four-momentum that is suggested by the magic-vector prescription of Aaron, Amado, and Young should not be used in off-mass-shell systems because it and the total four-momentum do not constitute a complete set of variables for the two-body system.