Spontaneous Fermion Production by a Supercritical Potential Well

TL;DR

This paper develops a quantum field theory framework to describe spontaneous positron production in supercritical potential wells, highlighting the physical mechanisms and differences from pair production.

Contribution

It introduces a formalism for calculating positron emission amplitudes in deep, time-dependent potential wells within Dirac's hole theory, addressing supercritical conditions.

Findings

Positron production occurs naturally in supercritical wells.

A formalism for emission amplitude calculation is established.

Differences between positron production and pair creation are clarified.

Abstract

A second quantised theory of electrons and positrons in a deep time-dependent potential well is discussed. It is shown that positron production from the well is a natural consequence of Dirac's hole theory when the strength of the well becomes supercritical. A formalism is developed whereby the amplitude for emission of a positron of a given momentum can be calculated. The difference between positron production and electron-positron pair production is demonstrated. Considerations of the vacuum charge and of Levinson's theorem are required for a full description of the problem.