Effective lagrangian for a strong color-electric field inside a flux tube with quark confinement

Abstract

The Dirac equation of a quark moving in a covariantly constant color-electric field and subject to a confining force is solved in a flux-tube geometry. Reflection and transmission amplitudes are obtained from the asymptotic form of the Dirac wave function. The effective Lagrangian of this problem is derived in terms of the reflection coefficients which in turn are expressed in terms of the color-electric field and the parameters of the confining force. For a large radius of the tube, this Lagrangian acquires the same form as that derived by Schwinger, with the quark mass and the force acting on it replaced by the effective mass and the effective force. The finite size and confinement effects on the effective Lagrangian are studied qualitatively. The qq^- pair production rate is shown to differ from the expressions used in the literature.