General realization of N=4 supersymmetric quantum mechanics and its applications

Abstract

Based upon the general supercharges which involve not only generators C_j of the Clifford algebra C(4,0) with positive metric, but also operators of third order, C_j C_k C_l, the general form of N=4 supersymmetric quantum mechanics (SSQM), which brings out the richer structures, is realized. Then from them, an one-dimensional physical realization and a new multi-dimensional physical realization of N=4 SSQM are respectively obtained by solving the constraint conditions. As applications, N=4 dynamical superconformal symmetries, which possess both the N=4 supersymmetries and the usual dynamical conformal symmetries, are studied in detail by considering two simple superpotentials k/x and \omega x, and their corresponding superalgebraic structures, which are spanned by eight fermionic generators and six bosonic generators, are established as well.