Light Cone QED in a Homogeneous Electric Background

TL;DR

This paper provides an exact solution for the Dirac equation in a light cone-dependent electric field, enabling real-time analysis of pair creation, resolving prior ambiguities, and revealing novel non-analytic current behaviors in QED.

Contribution

It introduces the first exact mode function solutions for arbitrary light cone electric fields in any dimension, resolving the $p^+=0$ ambiguity and enabling real-time pair production calculations.

Findings

Pair creation occurs as a discrete, instantaneous event on the light cone.

The solution applies to electrons of any mass and in any spacetime dimension.

Expectation values of current operators depend non-analytically on the background field.

Abstract

I present an exact solution for the Heisenberg picture, Dirac electron in the presence of an electric field which depends arbitrarily upon the light cone time parameter $x^+ = (t+x)/\sqrt{2}$. This is the largest class of background fields for which the mode functions have ever been obtained. The solution applies to electrons of any mass and in any spacetime dimension. The traditional ampiguity at $p^+ = 0$ is explicitly resolved. It turns out that the initial value operators include not only $(I + \gamma^0 \gamma^1) \psi$ at $x^+ = 0$ but also $(I - \gamma^0 \gamma^1) \psi$ at $x^- = -L$. Pair creation is a discrete and instantaneous event on the light cone, so one can compute the particle production rate in real time. In $D=1+1$ dimensions one can also see the anomaly. Another novel feature of the solution is that the expectation value of the currents operators depends non-analytically upon the background field. This seems to suggest a new, strong phase of QED.