PIRSA:20030116

The quasi-local degrees of freedom of Yang-Mills theory

Riello, A. (2020). The quasi-local degrees of freedom of Yang-Mills theory. Perimeter Institute. https://pirsa.org/20030116

Riello, Aldo. The quasi-local degrees of freedom of Yang-Mills theory. Perimeter Institute, Mar. 26, 2020, https://pirsa.org/20030116 

          @misc{ pirsa_PIRSA:20030116,
            doi = {10.48660/20030116},
            url = {https://pirsa.org/20030116},
            author = {Riello, Aldo},
            keywords = {Quantum Gravity},
            language = {en},
            title = {The quasi-local degrees of freedom of Yang-Mills theory},
            publisher = {Perimeter Institute},
            year = {2020},
            month = {mar},
            note = {PIRSA:20030116 see, \url{https://pirsa.org}}
          }

Aldo Riello

Perimeter Institute for Theoretical Physics

Talk number
PIRSA:20030116
Collection
Talk Type
Subject
Abstract

Gauge theories possess nonlocal features that, in the presence of boundaries, inevitably lead to subtleties. In particular their fundamental degrees of freedom are not point-like. This leads to a non-trivial cutting (C) and sewing (S) problem: 
(C) Which gauge invariant degrees of freedom are associated to a region with boundaries? 
(S) Do the gauge invariant degrees of freedom in two complementary regions R and R’ unambiguously comprise *all* the gauge-invariant degrees of freedom in M = R ∪ R’ ? Or, do new “boundary degrees of freedom” need to be introduced at the interface S = R ∩ R’ ?
In this talk, I will address and answer these questions in the context of Yang-Mills theory. The analysis is carried out at the level of the symplectic structure of the theory, i.e. for linear perturbations over arbitrary backgrounds. I will also discuss how the ensuing results translate into a quasilocal derivation of the superselection of the electric flux through the boundary of a region, and into a novel gluing formula which constructively proves that no ambiguity exists in the gluing of regional gauge-fixed configurations.
Time allowing I will also address how the formalism generalizes the “Dirac dressing” of charged matter fields, and how, in the presence of matter, quasi-local “global” charges (as opposed to gauge charges) emerge at special (i.e. reducible) configurations.

This talk is based on arXiv:1910.04222, with H. Gomes (U. of Cambridge, UK).
See also arXiv:1808.02074, with H. Gomes and F. Hopfmüller (Perimeter)