Pair Production by a Constant External Field in Noncommutative QED

TL;DR

This paper investigates electron-positron pair production in noncommutative QED under a constant electromagnetic field, revealing that noncommutativity affects the pair production threshold at loop level but not at tree level.

Contribution

It provides explicit solutions to the noncommutative Dirac equation in a constant field and analyzes how noncommutativity influences pair production rates and thresholds.

Findings

Tree-level pair production rate unchanged by noncommutativity.

Loop corrections decrease the threshold electric field.

Well-defined asymptotic states and causal Green's function established.

Abstract

In this paper we study QED on the noncommutative space in the constant electro-magnetic field background. Using the explicit solutions of the noncommutative version of Dirac equation in such background, we show that there are well-defined in and out -going asymptotic states and also there is a causal Green's function. We calculate the pair production rate in this case. We show that at tree level noncommutativity will not change the pair production and the threshold electric field. We also calculate the pair production rate considering the first loop corrections. In this case we show that the threshold electric field is decreased by the noncommutativity effects.