  It is possible to define a general initial state for a quantum field by
introducing a contribution to the action defined at an initial-time boundary.
The propagator for this theory is composed of two parts, one associated with
the free propagation of fields and another produced by the operators of this
initial action. The derivation of this propagator is shown for the case of a
translationally and rotationally invariant initial state. In addition to being
able to treat more general states, these techniques can also be applied to
effective field theories that start from an initial time. The eigenstates of a
theory with interacting heavy and light fields are different from the
eigenstates of the theory in the limit where the interactions vanish.
Therefore, a product of states of the noninteracting heavy and light theories
will usually contain excitations of the heavier state once the interactions are
included. Such excitations appear as nonlocal effects in the effective theory,
which are suppressed by powers of the mass of the heavy field. By appropriately
choosing the initial action, these excitations can be excised from the state
leaving just effects that would be produced by a local action of the lighter
fields.
