Initial state propagators

Abstract

It is possible to define a general initial state for a quantum field by introducinga 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.