MINISUPERSPACE APPROACH TO QUANTUM BUBBLE DYNAMICS

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 Aμvp. 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 Aμvp 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. © 1990.