Superconformal mechanics and nonlinear supersymmetry

We show that a simple change of the classical boson-fermion couplingconstant, $2\alpha \to 2\alpha n $, $n\in \N$, in the superconformal mechanicsmodel gives rise to a radical change of a symmetry: the modified classical andquantum systems are characterized by the nonlinear superconformal symmetry. Itis generated by the four bosonic integrals which form the so(1,2) x u(1)subalgebra, and by the 2(n+1) fermionic integrals constituting the two spin-n/2so(1,2)-representations and anticommuting for the order n polynomials of theeven generators. We find that the modified quantum system with an integer valueof the parameter $\alpha$ is described simultaneously by the two nonlinearsuperconformal symmetries of the orders relatively shifted in odd number. Forthe original quantum model with $|\alpha|=p$, $p\in \N$, this means thepresence of the order 2p nonlinear superconformal symmetry in addition to theosp(2|2) supersymmetry.Comment: 16 pages; misprints corrected, note and ref added, to appear in JHE