Gauge fixation and global phase time for minisuperspaces

Homogeneous and isotropic cosmological models whose Hamilton-Jacobi equatio n is separable are deparametrized by turning their action functional into t hat of an ordinary gauge system. Canonical gauge conditions imposed on the gauge system are used to define a global phase time in terms of the canonic al coordinates and momenta of the minisuperspaces. The procedure clearly sh ows how the geometry of the constraint surface restricts the choice of time ; the consequences that this has on the path integral quantization are disc ussed. (C) 1999 American Institute of Physics. [S0022-2488(99)00709-4].