A super-integrable discretization of the Calogero model

A time discretization that preserves the super-integrability of the Calogero model is obtained by application of the integrable time discretization of the harmonic oscillator to the projection method for the Calogero model with continuous time. In particular, the difference equations of motion, which provide an explicit scheme for time integration, are explicitly presented for the two-body case. Numerical results exhibit that the scheme conserves all the (=3) conserved quantities of the (two-body) Calogero model with a precision of the machine epsilon times the number of iterations. [PUBLICATION ABSTRACT]