Superconformal mechanics from N-extended Euler-Calogero-Moser and Calogero models

In this paper, we considered two-particle variants of the N-extended Euler-Calogero-Moser and Calogero models. Due the translation invariance, the center of mass can be decoupled (together with the corresponding fermions), leaving us with specific superconformal mechanics. Additional bosonic variables (spin variables) can easily be incorporated into the supercharges and the Hamiltonian. In the case of the Euler-Calogero-Moser model, the supersymmetry in the two-particle cases admits an unexpected extension from Osp(N|2) to SU(1,1|N) superconformal symmetry. The case of the Calogero model leads to purely Osp(N|2) superconformal mechanics. The way to get rid of the well-known problems along this path is to have a higher number of fermions present in the system.