Osp(2/1;C) graded Lie algebra and its intended applications to Yang-Mills theory

Abstract:
We construct explicitly the grade star Hermitian adjoint representation of osp(2/1;C) graded Lie algebra. Based on this a graded Yang-Mills field strength is defined. Its even part coincides with the field strength of the proper Lie subalgebra, su(2), of osp(2/1;C). We show that a pair of Grassman-odd scalar fields can be treated as a constituent part of the graded gauge potential on the equal footing with and ordinary (Grassman-even) one-form with values in the proper Lie subalgebra of graded Lie algebra osp(2/1;C). Action of gauge transformations on the defined field strength and Baker-Campbell -Hausdorff formula are considered, some possibilities of defining a meaningful variation principle are discussed.