On an inconsistency in path integral bosonization

TL;DR

This paper critically examines path integral bosonization in QCD, revealing that gluons must be composed of two quarks, which contradicts the fundamental independence of quarks and gluons in QCD.

Contribution

It demonstrates, without approximations, that gluons are composed of two quarks and explores the implications of Fierz reordering in bosonization, challenging conventional understanding.

Findings

Gluons are shown to be composed of two quarks.

Bosonization of Fierz reordered interactions yields gluons.

Colorless mesons are Fierz equivalent to a subset of gluons.

Abstract

A critically discerning discussion of path integral bosonization is given. Successively evaluating the conventional path integral bosonization of QCD it is shown without any approximations that gluons must be composed of two quarks. This contradicts the fundamentals of QCD, where quarks and gluons are independent fields. Furthermore, bosonizing the Fierz reordered effective four quark interaction term yields gluons, too. Colorless ``mesons'' are shown to be Fierz equivalent to a submanifold of gluons. The results obtained are not specific to QCD, but apply to other models as well.