GROUP THEORETICAL FOUNDATIONS OF FRACTIONAL SUPERSYMMETRY

Fractional supersymmetry denotes a generalization of supersymmetry whi ch may be constructed using a single real generalized Grassmann variab le, theta=<(theta)over bar>,theta(n)=0, for arbitrary integer n=2,3,.. .. An explicit formula is given in the case of general n for the trans formations that leave the theory invariant, and it is shown that these transformations possess interesting group properties. It is shown als o that the two generalized derivatives that enter the theory have a ge ometric interpretation as generators of left and right transformations of the fractional supersymmetry group. Careful attention is paid to s ome technically important issues, including differentiation, that aris e as a result of the peculiar nature of quantities such as theta. (C) 1996 American Institute of Physics.