Supersymmetry in Commutative and Non-commutative QFT

The research program is devoted to study systematically possible supersymmetric structures in commutative and non-commutative field theories. In this connection we intend to investigate: I. Topological field theories on ordinary and non-commutative manifolds Study of the vectorsupersymmetry in commutative and noncommutative topological quantum field models within the framework of perturbation theory and algebraic renormalization. II. Supersymmetric field theories on non-commutative spaces Investigations of various models of supersymmetric field theories using a superfield formulation with non- commutative four dimensional coordinates. III. Quantum Action Principe (QAP) and non-commutative geometry The possible existence of a QAP in the realm of non-commutative geometry for non-supersymmetric and supersymmetric quantum field theories will be discussed.

The research program is devoted to study systematically possible supersymmetric structures in commutative and non-commutative field theories. In this connection we intend to investigate: 1. Topological field theories on ordinary and non-commutative manifolds Study of the vectorsupersymmetry in commutative and noncommutative topological quantum field models within the framework of perturbation theory and algebraic renormalization. 2. Supersymmetric field theories on non-commutative spaces Investigations of various models of supersymmetric field theories using a superfield formulation with non-commutative four dimensional coordinates. 3. Quantum Action Principe (QAP) and non-commutative geometry The possible existence of a QAP in the realm of non-commutative geometry for non-supersymmetric and supersymmetric quantum field theories will be discussed.