Dirac-Square-Root formulation of some types of minisuperspace quantum cosmology.

Mathematics – Probability

Scientific paper

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Cosmology: Quantum Gravity, Cosmology: Bianchi Models, Cosmology: Friedmann Universe

Scientific paper

The Dirac-Square-Root formulation of the Wheeler-DeWitt equations for three types of universes is presented. They are the Bianchi type-I, type-IX, and the closed Friedmann universe. Wave equations which are linear in the time-like variable α are obtained for the Bianchi type-I and type-IX spacetimes using purely geometrical coordinates. For the Friedmann cosmology, without adopting any additional coordinates, just a one-component wave equation is obtained. These equations give a conserved current with a positive-definite probability density. Also, the possibility of the quaternionic Dirac-type equation is commented upon.

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