A New formulation of Quantum Gravity

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I have been working on the following four subjects under the above project : 1) We proposed (Kawamoto, Watabiki) new type of generalized gauge theories which could be formulated in any dimensions about 10 years ago. We quantized the generalized Chern-Simons action and found out that the system is infinitely reducible and can be quantized by introducing infinitely many ghosts yet has the same Chern-Simons form as the original classical action. We have then quantized the generalized topological Yang-Mills action with instanton gauge fixing and found that N=2 super-Yang-Mills action comes out as a natural consequence of the the quantization via twisting procedure. We found the twinsting is essentitally related with Dirac-Kahler fermion formulation. 2) We have successfully formulated the three-dimensional Chern-Simons gravity on the random lattice. It turned out that the model is equivalent with the Ponzano-Regge model. We have then successfully applied this formulation into four dimensional BF gravity on the random lattice. 3) We have investigated two dimensional quantum gravity coupled c=-2 matter numerically with great accuracy. We have learned that the essense of the two dimensional quantum gravity is the fractal nature and the numerical fractal dimensions are consistent with the theoretical prediction. The three dimensional extension of this model is investigated numerically. We measured the string susceptibility and found an evidence that there exists a continuum limit of the three dimensional lattice gravity. 4) We have extended the generalized gauge theory to formulate the generalized Yang-Mills action and applied to formulate Weinberg-Salam model successfully by using SU(2|1) super group.