  We consider two technical developments of the formalism of continuous-time
histories. First, we provide an explicit description of histories of the simple
harmonic oscillator on the classical histories phase space, comparing and
contrasting the Q, P and Wigner representations; we conclude that a
representation based on coherent states is the most appropriate. Second, we
demonstrate a generic method for implementing a perturbative approach for
interacting theories in the histories formalism, using the quartic anharmonic
oscillator. We make use of the identification of the closed-time path (CTP)
generating functional with the decoherence functional to develop a perturbative
expansion for the latter up to second order in the coupling constant. We
consider both configuration space and phase space histories.
