QUANTUM STATE OF A NUCLEATING BUBBLE

We consider a field theory consisting of two interacting scalar fields: sigma and phi. The scalar field sigma is assumed to undergo a first-order phase transition via the nucleation of bubbles. We solve the Schrodinger equation for the combined system of a bubble plus the field phi with appropriate boundary conditions. This allows us to determine the quantum state of the field phi in the background of the nucleating and subsequently expanding bubble. The simplest description of this quantum state is obtained in the picture where phi is represented as an infinite set of massive scalar fields in a (2 + 1)-dimensional de Sitter space. We show that the bubble nucleates with all these fields in de Sitter-invariant quantum states and that the resulting quantum state of the field phi is Lorentz invariant.