DIRAC-SQUARE-ROOT FORMULATION OF SOME TYPES OF MINISUPERSPACE QUANTUMCOSMOLOGY

The Dirac-Square-Root formulation of the Wheeler-DeWitt equations for three types of universes is presented. They are the Bianchi type-I, ty pe-IX, and the closed Friedmann universe. Wave equations which are lin ear in the time-like variable Lu are obtained for the Bianchi type-I a nd type-IX spacetimes using purely geometrical coordinates. For the Fr iedmann cosmology,;without adopting any additional coordinates, just a one-component wave equation is obtained. These equations give a conse rved current with a positive-definite probability density. Also, the p ossibility of the quaternionic Dirac-type equation is commented upon.