Time and Energy

Abstract

Space and time have a double role in quantum mechanics. On the one hand, they form the arena for physical events; physical systems occur in spacetime. On the other hand, the symmetries of the underlying spacetime specify the description of the system and dictate its basic properties. In the relativistic case spacetime symmetries are expressed with respect to the Poincaré group, while in the nonrelativistic case the relevant symmetry group is the Galilei group. This Chap. 17 presents an analysis of covariant time observables in the case of classical Hamiltonian mechanics and analogous considerations in quantum mechanics.