Effective Lagrangian with valence gluons in extended SU(2) QCD model

TL;DR

This paper derives an effective Lagrangian for valence gluons in an extended SU(2) QCD model, maintaining gauge and Lorentz invariance, and finds it acquires a positive imaginary component.

Contribution

It introduces a one-loop effective Lagrangian for valence gluons in extended SU(2) QCD, preserving gauge and Lorentz invariance throughout.

Findings

Effective Lagrangian obtained with positive imaginary part.

Maintains gauge and Lorentz invariance during calculation.

Includes quartic interaction terms in the analysis.

Abstract

The effective action with homogeneous valence (off-diagonal) gluons as background fields in the extended SU(2) model of QCD is obtained in one-loop approximation. We keep the manifest gauge and Lorentz invariance during whole calculation by using a special gauge-fixing recipe and taking into account the quartic interaction terms in the original Lagrangian as well. It has been shown that the effective Lagrangian gains a positive imaginary part.