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The quasilocal degrees of freedom of Yang-Mills theory

by Henrique Gomes, Aldo Riello

Submission summary

As Contributors: Henrique Gomes · Aldo Riello
Preprint link: scipost_202001_00038v3
Date accepted: 2021-05-31
Date submitted: 2021-05-17 17:18
Submitted by: Riello, Aldo
Submitted to: SciPost Physics
Academic field: Physics
  • High-Energy Physics - Theory
  • Mathematical Physics
Approach: Theoretical


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: (\textit{1}) characterize a basis for quasilocal degrees of freedom (dof) that is manifestly gauge-covariant also at the boundary; (\textit{2}) tame the non-additivity of the regional symplectic forms upon the gluing of regions; and to (\textit{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.

Published as SciPost Phys. 10, 130 (2021)

Author comments upon resubmission

First, we would like to thank again the referee for the comments which were instrumental for the sharpening the paper.
We attach our answers to this second, brief, round of comments.

List of changes

We have corrected the more perfunctory comments and answered the more substantial ones as follows (the numbering follows the referee's report):

(2) We added a brief paragraph at the beginning of section 2 to clarify the scope of the functional space we work in.

(3) After eq (1) we removed reference to temporal gauge.

(4) We corrected the accidental mischaracterization of P = A/G as the reduced phase space.

(6) We kept reference to the (extremely) general space of forms solely as an example that does not reoccur.

(7-8) We added two short paragraphs ("We refer to..." and "Mathematically...")) at the end of section 3.4 clarifying the status of the “canonical completion” and symplectic reduction in the presence of boundaries. However, we kept reference [20] as the main source of details on the topic.

Reports on this Submission

Anonymous Report 1 on 2021-5-18 (Invited Report)


All of my previous comments have been answered.
I do recommend this article for publication in Scipost.

  • validity: high
  • significance: high
  • originality: high
  • clarity: high
  • formatting: perfect
  • grammar: perfect

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