Schwinger Pair Production and Fall to the Center

Abstract

The classical field theory of Schwinger pair creation can be described using an effective Schrodinger equation with an inverted harmonic oscillator Hamiltonian. It is a well known fact that the inverted harmonic oscillator admits a canonical transformation to a Q.P type Berry-Keating Hamiltonian. In this thesis we demonstrate that the classical field theory of Schwinger pair creation has a hidden scale invariance described by the quantum mechanics of an attractive inverse square potential in the canonically rotated (Q,P) coordinates of the inverted harmonic oscillator. The quantum mechanics of the inverse square potential is well known because of the problem of fall to the center and the associated ambiguities in the boundary condition. It is also well known as a description of the physics of pair creation in the presence of an event horizon and black hole decay. We use point particle effective field theory (PPEFT) to derive the boundary condition which describes pair creation. This leads to the addition of an inevitable Dirac delta function with imaginary coupling to the inverse square potential, describing the physics of the source. This non-hermitian physics leads to the Klein paradox. The conservation loss is due to the charged pairs being produced during tunneling.