Evolution and covariance in constraint dynamics

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Abstract
Two problems of first-class relativistic constraint dynamics of direct interaction are considered. The first is the relation of the gauge motion to the physical motion. In a manifestly covariant formulation they are shown to be exactly equivalent, the latter duplicating the former. The physical motion arises as a consequence of the explicit dependence on an (invariant) time parameter introduced by the gauge fixations (specification of "equal-time" surfaces). No simple relation exists in general between the evolution generator and the translation generators. The second problem deals with the covariance of the physical world lines. It is satisfied trivially for Lorentz covariance (since the formalism is covariant) and can be satisfied nontrivially for translations in the equal-time surface orthogonal to the total momentum. Sufficient conditions on the fixations are given to ensure such covariant world lines.