Resolving the $p^{+}=0$ Ambiguity in a Homogeneous Electric Background

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 ambiguity 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 current operators depends nonanalytically upon the background field. This seems to suggest a new, strong phase of QED.

5 pages, LaTeX 2 epsilon, 2 figures, talk presented at the International Workshop on Light-cone Physics, Particles and Strings, Trento, Italy, Sept. 3-11, 2001

References in corpus (2)

• Pair creation and axial anomaly in light-cone $QE{D}_2$
• Light Cone QED in a Homogeneous Electric Background

Cited by in corpus (6)

• Exact classical and quantum dynamics in background electromagnetic fields
• Localisation in worldline pair production and lightfront zero-modes
• Pair production: the view from the lightfront
• Reduction of order, resummation and radiation reaction
• Exact solutions in radiation reaction and the radiation-free direction
• Reduction of Order and Transseries Structure of Radiation Reaction