Gluon propagator and effective Lagrangian in quantum chromodynamics

Considering the one-loop effective action up to order ${g}^{2}$ in external color fields, one finds a negative imaginary part of the effective action for color electric fields. We discuss the compatibility of this result with the requirement that the absolute value of the vacuum-vacuum amplitude must not exceed one. In order to evaluate the exact one-loop effective Lagrangian for homogeneous color fields, we study extensively the gluon propagator in a homogeneous color field. We find a negative imaginary part of the effective Lagrangian in a homogeneous color electric field, whereas the imaginary part of the effective Lagrangian in a homogeneous color magnetic field vanishes. (This is opposed to the results published so far in the existing literature.) We further discuss the appearance of gluon pair annihilation in color electric fields and explain it by the antiscreening effect.

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