Boundary terms in quantum field theory and the spin structure of QCD

TL;DR

This paper investigates the behavior of boundary terms in quantum field theories, establishing conditions for their vanishing, and applies this to analyze the physical meaningfulness of quark-gluon angular momentum decomposition in QCD.

Contribution

It provides a necessary and sufficient condition for boundary terms to vanish in QFT and applies this to clarify the non-perturbative structure of QCD affecting angular momentum decomposition.

Findings

Boundary terms do not generally vanish in quantum field theories.

The quark-gluon angular momentum decomposition in QCD is not physically meaningful due to non-perturbative effects.

Classical arguments for boundary terms are insufficient in quantum theories.

Abstract

Determining how boundary terms behave in a quantum field theory (QFT) is crucial for understanding the dynamics of the theory. Nevertheless, boundary terms are often neglected using classical-type arguments which are no longer justified in the full quantum theory. In this paper we address this problem by establishing a necessary and sufficient condition for arbitrary spatial boundary terms to vanish in a general QFT. As an application of this condition we examine the issue of whether the angular momentum operator in Quantum Chromodynamics (QCD) has a physically meaningful quark-gluon decomposition. Using this condition it appears as though this is not the case, and that it is in fact the non-perturbative QCD structure which prevents the possibility of such a decomposition.