Relation between tunneling and particle production in vacuum decay - art. no. 123521.

The field-theoretical description of quantum fluctuations on the background of a tunneling field sigma is examined in the case of a functional Schrodi nger approach. We apply;this method in the case when quantum fluctuations a re coupled to the sigma field through a mass-squared term, which is "time d ependent" since we include the dynamics of sigma. The resulting mode functi ons of the fluctuation field, which determine the quantum state after tunne ling, display a previously unseen resonance effect when their mode number i s comparable to the curvature scale of the bubble. A detailed analysis of t he relation between the excitations of the field about the true vacuum (int erpreted as particle creation) and the phase shift coming from tunneling is presented. [S0556-2821(99)02112-8].