Canonical (anti-)commutation rules in QCD and unbroken gauge invariance, QCD - the two central anomalies and canonical structure

TL;DR

This paper explores how large-distance gauge invariance in QCD influences the canonical structure and demonstrates that the trace anomaly necessitates modifications to the gauge boson Lagrangian and canonical rules.

Contribution

It reveals the impact of gauge invariance and trace anomaly on the canonical commutation relations and the Lagrangian structure in QCD.

Findings

Gauge invariance constrains canonical representations in QCD.

Trace anomaly modifies the gauge boson Lagrangian.

Canonical structure is altered by large-distance regularities.

Abstract

The regularities at large distances of complete gauge invariance in QCD are shown to bear nontrivial consequences for the selection among inequivalent representations of canonical commutation (anticommutation) rules for gauge boson (quark) fields. The trace anomaly forces a modification of the gauge boson Lagrangean and by this of the entire associated canonical structure.