Physical states in canonically quantized , finite , 4 dimensional quantum gravity . Quantized constraints of the full theory

Physical states in canonically quantized, finite, 4 dimensional quantum gravity. Quantized constraints of the full theory. Abstract This is the first in a series of papers outlining an algorithm to explicitly construct a finite quantum theory of gravity in Ashtekar variables. The algorithm is based upon extending some properties of a special state, the Kodama state for pure gravity with cosmological term, to more general models. We then illustrate a presciption for nonperturbatively constructing the analogue of the Kodama state for a general case, in preparation for subsequent works in this series. We also touch in the last section upon some issues in quantum gravity which may be addressed within the context of our approach, mainly for future work in the seires. These include issues of finiteness, renormalizability, reality conditions on the Ashtekar variables and the problem of time in quantum gravity.