Path-integral quantum cosmology. I. Vacuum Bianchi type I

The Feynman path-integral formalism is applied to study the quantum mechanics of the vacuum Bianchi type-I cosmological model. A measure is obtained for the functional integral representing the minisuperspace transition amplitude which allows the performance of the Arnowitt-Deser-Misner (ADM) reduction within the path integral. This requires a careful analysis of the roles played by the original coordinate time and the intrinsic minisuperspace time. The role of the imposed Feynman boundary conditions is discussed. The integrals are all evaluated to obtain the transition amplitude in closed form. An alternative scheme for evaluation of the transition amplitude is presented to avoid problems related to the nonpolynomial nature of the ADM Hamiltonian.