Towards A New Formulation of Unified Model with Gravity on a Lattice

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My research thema in this period can be classified into the following 4 categories :1)Continuation from the previous investigations.2)Fermion Formulation with Non-commutativity on a Lattice.3)A Proposal of New Superspace Formulation.4)Supersymmetry on a Lattice.1)Based on the generalized gauge theory formulation which we discovered, we applied a truncated version of generalized Yang-Mills theory with SU(2|1) gauge group and derived Weinberg-Salam model. Numerical evaluation of the c-dependence of the fractal dimension of two-dimensional quantum surface was investigated and the result is perfect agreement with the analytic result which we obtained previously.2)We may introduce mild non-commutativity for the lattice difference operator tosatisfy the Leibniz rule. We can then define differential form on a lattice and introduce associative Clifford product. We have clarified the Dirac-Kahler fermion formulation with non-commutativity on a lattice.3)It was already recognized that the twisting appeared in the quantization of topological field theory can be identified as a Dirac-Kahler fermion formulation. We found that this twisting mechanism is a universal characteristic which appears in the quantization of topological field theory and a twisted superspace formulation is hidden behind the formulation. N=2 twisted superspace formulation was formulated in two dimensions. Then this formulation is extended into N=4 in four dimensions.4)Twisted superspace formulation is successfully formulated on a lattice with the introduction of the mild non-commutatibity for N=2 twisted superspace in two dimensions. It is now possible to apply this formulation to N=2 super Yang-Mills action on a lattice.