Nonlinear superconformal symmetry of a fermion in the field of a Dirac monopole

We study a longstanding problem of identification of the fermion-monopole symmetries. We show that the integrals of motion of the system generate a nonlinear classical Z(2)-graded Poisson, or quantum superalgebra, which may be treated as a nonlinear. generalization of the osp(2\2) circle plus su(2). In the nonlinear superalgebra, the shifted square of the full angular momentum plays the role of the central charge. Its square root is the even osp(2\2) spin generating the u(1) rotations of the supercharges. Classically, the central charge's square root has an odd counterpart whose quantum analog is, in fact, the same osp(2\2) spin operator. As an odd integral, the osp(2\2) spin generates a nonlinear supersymmetry of De Jonghe, Macfarlane, Peeters and van Holten, and may be identified as a grading operator of the nonlinear superconformal algebra. (C) 2004 Published by Elsevier B.V.