Time as spacetime four-volume and the Ashtekar variables

We consider a recently proposed theory of gravity, classically equivalent to Einstein's theory with the cosmological constant as an additional variable, in which spacetime volume plays the role of time. We develop a Hamiltonian formulation using Ashtekar's variables, set up the corresponding quantum theory, and show that the known loop state solutions of quantum general relativity are also solutions in the present theory. We conclude with some remarks on why we feel that this quantum theory deserves further study.