Covariant factor ordering of gauge systems using ghost variables. I. Constraint rescaling

<jats:p>A dynamical consequence of local gauge invariance is the existence of first class constraints that are linear in momenta. By studying finite-dimensional systems with this constraint structure one finds that, in order to quantize such theories, it is not enough to find a consistent factor ordering, rather, one must also maintain covariance under rescaling of the constraints, point transformations, and weak changes to the observables. Within the standard Dirac constraint formalism, covariance under these symmetries obstructs a full Hilbert space description. It is shown how this difficulty may be overcome by the use of ghost variables. In the present paper, I, an analysis of the Becchi–Rouet–Stora–Tyutin (BRST) structure of such systems is presented. The constraint rescaling is shown to be implemented by a canonical transformation on the super phase space that can be evaluated to a unitary transformation on a suitably defined state space. In the following paper, II [J. Math. Phys. 30, xxx (1989)] these techniques are used to solve the constraint factor ordering problem.</jats:p>