An Action for the Infrared Regime of Gauge Theories and the Problem of Color Transformations

TL;DR

This paper explores the infrared behavior of gauge theories, demonstrating that color transformations cannot be unitarily implemented on low-energy gluon states, with implications for confinement and the mass gap.

Contribution

It introduces an action formalism with a diffeomorphism for hard gauge particles and matter fields, analyzing infrared issues and color transformations in nonabelian gauge theories.

Findings

Color transformations are not unitarily implementable on low-energy gluon states.

Re-derivation of Lorentz symmetry breaking in QED's charged sectors.

Implications discussed for confinement and the mass gap.

Abstract

It has been known for a while that there is spontaneous breaking of Lorentz symmetry in the nonzero charged sectors of quantum electrodynamics due to the infrared problem of soft photons. More recently, it has also been suggested that similar results hold for color transformations in a nonabelian gauge theory. Here we show that an action where a diffeomorphism has been carried out for the part describing hard gauge particles and matter fields can be used to analyze these issues. In addition to rederiving old results in this formalism, we also show that color transformations cannot be unitarily implemented on perturbative gluon states if gluon fields of arbitrarily low energy are allowed. Implications for confinement and mass gap are briefly commented upon.