Superconformal Calogero Models as a Gauged Matrix Mechanics

Abstract

We present basics of the gauged superfield approach to constructing the N-superconformal multi-particle Calogero-type systems developed in arXiv:0812.4276, arXiv:0905.4951 and arXiv:0912.3508. This approach is illustrated by multi-particle
systems possessing SU(1, 1|1) and D(2, 1; α) supersymmetries, as well as by the model of new N = 4 superconformal quantum mechanics.