Report on scipost_202001_00038v1

Abstract

Gauge theories possess nonlocal features that, in the presence of boundaries, inevitably lead to subtleties. In the D + 1 formulation of Yang-Mills theories, we employ a generalized Helmholtz decomposition rooted in the functional geometry of the theory's configuration space to (i ) identify the quasilocal radiative and pure-gauge/Coulombic components of the gauge and electric fields, and to (ii ) fully characterize the properties of these components upon gluing of regions. The analysis is carried out at the level of the symplectic structure of the theory, i.e. for linear perturbations over arbitrary backgrounds. Contents 4.4 Gluing of the electric field 36 4.5 On the energy of radiative and Coulombic modes 38 4.6 Gluing of the symplectic potentials 39 4.7 Example: 1-dimensional gluing and the emergence of topological modes 41 5 Conclusions 44 5.1 Summary 44 5.2 Outlook 48 A Time dependent gauge transformations 50 B Computation of the symplectic form 52 C Proof of equation (60) 53 D The SdW connection from the Dirac dressing 54 References 58