  We define the action operator in the consistent histories formalism, as the
quantum analogue of the classical action functional, for the simple harmonic
oscillator case. The action operator is shown to be the generator of time
transformations, and to be associated with the two types of time-evolution of
the standard quantum theory: the wave-packet reduction and the unitary
time-evolution. We construct the corresponding classical histories and
demonstrate the relevance with the quantum histories. Finally, we show the
relation of the action operator to the decoherence functional.
