The quasilocal degrees of freedom of Yang-Mills theory

TL;DR

This paper uses geometric methods to analyze the boundary and nonlocal features of Yang-Mills theories, clarifying the structure of degrees of freedom and their role in gauge and global charges.

Contribution

It introduces a gauge-covariant basis for quasilocal degrees of freedom and explains the non-additivity of symplectic forms in Yang-Mills theories.

Findings

Splits Yang-Mills dof into Coulombic and radiative components.

Identifies non-locality as the source of symplectic non-additivity.

Links the dof split to Dirac's dressed electron.

Abstract

Gauge theories possess nonlocal features that, in the presence of boundaries, inevitably lead to subtleties. We employ geometric methods rooted in the functional geometry of the phase space of Yang-Mills theories to: (1) characterize a basis for quasilocal degrees of freedom (dof) that is manifestly gauge-covariant also at the boundary; (2) tame the non-additivity of the regional symplectic forms upon the gluing of regions; and to (3) discuss gauge and global charges in both Abelian and non-Abelian theories from a geometric perspective. Naturally, our analysis leads to splitting the Yang-Mills dof into Coulombic and radiative. Coulombic dof enter the Gauss constraint and are dependent on extra boundary data (the electric flux); radiative dof are unconstrained and independent. The inevitable non-locality of this split is identified as the source of the symplectic non-additivity, i.e. of the appearance of new dof upon the gluing of regions. Remarkably, these new dof are fully determined by the regional radiative dof only. Finally, a direct link is drawn between this split and Dirac's dressed electron.