Realization of lattice supersymmetry with over degree of freedom

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The result of this project is listed as the followings;1. Translational invariant and local lattice filed theories have been formulated.2. Ordinary Leibniz rue cannot be held with finite flavor on translational invariant and local lattice theory.3. The matrix representation of the lattice theory as the lattice size flavor one satisfying with Leibniz rule is neccessarily nonlocal theory after the continuum limit.4. Another local lattice framwork with Kaluza-Klein modes is also inconsistent with the Leibniz rule5. The only possiblity for the lattice supersymmetry with locality is to rebuild a Leibniz rule in the lattice proper formalism.