PIRSA:20030116 Scientific Series Quantum Gravity

DOI10.48660/20030116

Series: Quantum Gravity

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}}
}

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)

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