A Realization of the infinite-dimensional symmetries of conformal mechanics

We discuss the possibility of realizing the infinite dimensional symmetries of conformal mechanics as time reparametrizations, generalizing the realization of the $\mathrm{SL}(2,\mathbf{R})$ symmetry of the de Alfaro\char21{}Fubini\char21{}Furlan model in terms of quasiprimary fields. We find that this is possible using an appropriate generalization of the transformation law for the quasiprimary fields.