A new superconformal mechanics

In this paper we propose a new supersymmetric extension of conformal mechan ics. The Grassmannian variables that we introduce are the basis of the form s and of the vector fields built over the symplectic space of the original system. Our supersymmetric Hamiltonian itself turns out to have a clear geo metrical meaning being the Lie derivative of the Hamiltonian flow of confor mal mechanics. Using superfields we derive a constraint which gives the exa ct solution of the supersymmetric system in a way analogous to the constrai nt in configuration space which solved the original nonsupersymmetric model . Besides the supersymmetric extension of the original Hamiltonian, we also provide the extension of the other conformal generators present in the ori ginal system. These extensions also have a supersymmetric character being t he square of some Grassmannian charge. We build the whole superalgebra of t hese charges and analyze their closure. The representation of the even part of this superalgebra on the odd part turns out to be integer and not spino rial in character. (C) 2000 American Institute of Physics. [S0022-2488(00)0 2612-8].