Some remarks on the use of effective Lagrangians in QED and QCD

TL;DR

This paper explores alternative methods for deriving effective Lagrangians in QED and QCD, emphasizing the use of the energy-momentum tensor and leading-log models over traditional computational techniques, and questions the validity of certain lattice QCD approaches.

Contribution

It introduces a simplified approach to calculate effective Lagrangians without constant field assumptions and critically examines the use of covariant constant fields in lattice QCD.

Findings

Effective Lagrangians can be derived without constant external fields.

The energy-momentum tensor and leading-log model provide practical alternatives.

Critiques the reliance on covariant constant fields in lattice QCD for QCD vacuum studies.

Abstract

We discuss in this article the usefulness of the effective Lagrangians (L_eff) of QED and QCD within the one-loop approximation. Instead of calculating L_eff via complicated computations with Schwinger's proper-time technique or Feynman graphs, we prefer to employ the energy-momentum tensor and the leading-log model. The advantage is that we do not have to demand the external electromagnetic or color field to be constant. There are also some critical remarks added which cast doubt on the use of LQCD with covariant constant fields in explaining the nature of the QCD vacuum.