Minisuperspace approach to quantum bubble dynamics

Abstract

The minisuperspace approximation, widely used in quantum cosmology, is used to study the properties of the wave function of a spherically symmetric quantum bubble. The case of the free bubble illustrtes the method which is then applied to the case of a bubble minimally coupled to the totally anti-symmetric tensor gauge potential A μvp . The minisuperspace approximation fully preserves the relativistic properties of bubble dynamics but reduces the problem to that of the motion of a relativistic point-particle in an external electromagnetic potential in 1 + 1 dimensions. In this conncetion we discuss the analogue of the Klein effect for quantum bubbles: while a free bubble can exist in discrete levels of positive energy, with large bubbles being exponentially depressed, the interaction with the A μvp potential leads to the crossing of positive and negative energy levels; this phenomenon gives rise to a finite probability that a bubble might tunnel to a classical configuration of arbitrarily large radius.