Vacuum decay induced by quantum fluctuations

Abstract

We treat the effects of quantum field fluctuations on the decay of a metastable state of a self-coupled scalar field. We consider two varieties of field fluctuations and their potential effects in a semiclassical description. The first are the fluctuations of the time derivative of a free massive scalar field operator, which has been averaged over finite regions of space and time. These fluctuations obey a Gaussian probability distribution. A sufficiently large fluctuation is assumed to produce an effect analogous to a classical initial field velocity, which can cause a finite region to fly over the barrier separating the metastable state from the stable vacuum state. Here we find a contribution to the decay rate which can be comparable to the decay rate by quantum tunneling, as computed in an instanton approximation. This result is consistent with those of other authors. We next consider the effects of the fluctuations of operators which are quadratic in the time derivative of the free scalar field. The quadratic operator is also averaged over finite regions of space and of time. Now the probability distribution for the averaged operator falls more slowly than an exponential function, allowing for the possibility of very large fluctuations. We find a contribution to the decay rate which, under certain conditions, may be larger than those coming from either quantum tunneling or linear field fluctuations.