Quantization of the Taub model with extrinsic time

The paper addresses the quantization of cosmological models, with application to the Taub model. By reducing the model with extrinsic time, a formalism is developed in order to define a conserved Schrödinger inner product in the space of solutions of the Wheeler-DeWitt equation. A quantum version of classical canonical transformations is introduced for connecting the solutions of the Wheeler-DeWitt equation with the wave functions of the reduced system. Once this correspondence is established, boundary conditions on the space of solutions of the Wheeler-DeWitt equation are obtained to directly select the physical subspace.