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.
Highlights
Schwinger effect [1] and phase transitions through bubble nucleation [2,3,4,5] are both nonperturbative effects in which a metastable state decays into an energetically favorable configuration
There is potential energy UðxÞ that can be characterized by a single variable x of dimension length, which measures the separation of the particles in the Schwinger pair or the radius of a bubble for the vacuum decay
The above quantum-mechanical-tunneling picture on Schwinger effect can be used to draw a close analogy to false vacuum decay in quantum field theory, which can be mapped onto a simple tunneling problem in onedimensional quantum mechanics in the same way
Summary
Schwinger effect [1] and phase transitions through bubble nucleation [2,3,4,5] are both nonperturbative effects in which a metastable state decays into an energetically favorable configuration. Phase transitions can be modeled in scalar quantum field theory as the decay of a metastable state known as “false vacuum,” where the scalar field represents an order parameter for the transition In both problems, there is potential energy UðxÞ that can be characterized by a single variable x of dimension length, which measures the separation of the particles in the Schwinger pair or the radius of a bubble for the vacuum decay. X is interpreted as the position of the particle, and the potential energy UðxÞ has to be complemented by a kinetic energy with a suitably defined effective mass In this picture, the same bounce solution can be used to compute B in both problems. Brief review of the Callan-Coleman method on quantum tunneling is given in the Appendix
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