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Supersymmetric field theories on noncommutative spaces are constructed. We present two different representations of noncommutative space, but we can obtain supersymmetry algebla and supersymmetric Yang-Mills action independent of its representation. As a result, we will see that the action has a close relationship with IIB matrix model.
Comment: 23 pages, Greatly Improved on 4 Nov 2001
Comment: Proceeding of International Workshop "Frontier of Quantum Physics" February 17(Thu.)-19(Sat.) 2005
Comment: 25 pages, New section and some references are added. Some comments are added
We present an attempt to formulate the supersymmetric and relativistic quantum mechanics in the sense of realizing supersymmetry on the single particle level, by utilizing the equations of motion which is equivalent to the ordinary 2nd quantization of the chiral multiplet. The matrix formulation is used to express the operators such as supersymmtry generators and fields of the chiral multiplets. We realize supersymmetry prior to filling the Dirac sea.
Comment: Proceeding of the International Workshop, "Frontier of Quantum Physics" 17-19 Feb. 2005, Kyoto, Japan
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