Physical states in canonically quantized , finite , 4 dimensional quantum gravity

Physical states in canonically quantized, finite, 4 dimensional quantum gravity. Minisuperspace Asktekar–Klein–Gordon model. Abstract This is the second paper in a series outlining an algorithm to consistently quantize four dimensional gravity in Ashtekar variables. We put to use the machinery and techniques developed in the first paper for a simple example in minisuperspace, highlighting the some of the relevant features necessary to address the full theory such as functional integration in the space of fields and solution of the problem of time. We consider the case of a diagonal CDJ matrix and connection, observing the symmetries imposed upon each due to the mixed par-tials consistency condition. We then indicate how to write down the solution to the quantized Hamiltonian constraint for the generalized Kodama state for a homogeneous and isotropic connection for simplicity. In the last section we illustrate a solution for the semiclassical part of the Hamiltonian constraint for the case of a homogeneous and isotropic CDJ matrix in order to highlight solme of the features of the semiclassical orbits of the spacetime such as inflation.