Schwinger effect and false vacuum decay as quantum-mechanical tunneling of a relativistic particle

Abstract

We present a simple and intuitive description of both, the Schwinger effect and false vacuum decay through bubble nucleation, as tunneling problems in one-dimensional relativistic quantum mechanics. Both problems can be described by an effective potential that depends on a single variable of dimension length, which measures the separation of the particles in the Schwinger pair, or the radius of a bubble for the vacuum decay. We show that both problems can be described as tunneling in one-dimensional quantum mechanics if one interprets this variable as the position of a relativistic particle with a suitably defined effective mass. The same bounce solution can be used to obtain reliable order of magnitude estimates for the rates of the Schwinger pair production and false vacuum decay.

Comments: 11 pages, revtex format; v2: a discussion on the Schwinger effect in spatially inhomogeneous electric fields has been added, to match the published version