Schwinger effect for non-Abelian gauge bosons

Michael Ragsdale,Douglas Singleton

doi:10.1088/1742-6596/883/1/012014

Abstract

We investigate the Schwinger effect for the gauge bosons in an unbroken non-Abelian gauge theory (e.g. the gluons of QCD). We consider both constant “color electric” fields and “color magnetic” fields as backgrounds. As in the Abelian Schwinger effect we find there is production of “gluons” for the color electric field, but no particle production for the color magnetic field case. Since the non-Abelian gauge bosons are massless there is no exponential suppression of particle production due to the mass of the electron/positron that one finds in the Abelian Schwinger effect. Despite the lack of an exponential suppression of the gluon production rate due to the masslessness of the gluons, we find that the critical field strength is even larger in the non-Abelian case as compared to the Abelian case. This is the result of the confinement phenomenon on QCD.

Highlights

The Schwinger effect is considered for the gauge bosons in an unbroken non-Abelian gauge theory
The Schwinger effect [1] is the non-perturbative production of electron-positron pairs in an external electric field applied to a quantum electrodynamical vacuum
In this paper the Schwinger effect for SU (2) gluons was investigated. The motivation behind this was the massless nature of the gluons causing the effect to be more important than the standard Schwinger effect, which is exponentially suppressed due to the electron/positron rest mass

Summary

INTRODUCTION

The Schwinger effect is considered for the gauge bosons in an unbroken non-Abelian gauge theory. The Schwinger effect has not been observed experimentally in the form it was first calculated, a uniform background electric field producing electron-positron pairs. QCD is a non-Abelian gauge theory, with symmetry group SU (3) It is the theory of strong interactions, one of the fundamental forces of the Universe. The Schwinger effect [1] is the non-perturbative production of electron-positron pairs in an external electric field applied to a quantum electrodynamical vacuum. A similar expression can be obtained with the sum over all paths [dx] and Lagrangian replaced by a summation over all field configurations [dφ] and a volume integral over an appropriate Lagrange density d3xL(φ, ∂μφ) respectively [11] This yields amp(vac → vac) −T−→−∞→ const [dφ] exp i d4xL(φ, ∂μφ).

12 By using the representation of the logarithm

24 Taking this into account gives

25 Now replace A1μ and A2μ with the complex terms

27 Running through the indices for μ expands this to

DISCUSSION AND CONCLUSIONS