  It is well known that the time dependent harmonic oscillator possesses a
conserved quantity, usually called Ermakov-Lewis invariant. I provide a simple
physical interpretation of this invariant as well as a whole family of related
invariants. This interpretation does not seem to have been noticed in the
literature before. The procedure also allows one to tackle some key conceptual
issues which arise in the study of quantum fields in external, time dependent,
backgrounds like in the case of particle production in an expanding universe
and Schwinger effect.
