Conformal mechanics

The SL(2,R)$SL(2,\mathbb{R})$ invariant Hamiltonian systems are discussed within the framework of the orbit method. It is shown that both the dynamics and the symmetry transformations are globally well-defined on phase space. The flexibility in the choice of the time variable and the Hamiltonian function described in the paper by de Alfaro et al. Nuovo Cimento 34A (1976) 569] is related to the nontrivial global structure of 1+0$1+0$-dimensional space–time. The operational definition of time is discussed.