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Edge modes as dynamical frames: charges from post-selection in generally covariant theories
by Sylvain Carrozza, Stefan Eccles, Philipp A. Hoehn
Submission summary
| Authors (as registered SciPost users): | Sylvain Carrozza · Stefan Eccles |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2205.00913v2 (pdf) |
| Date submitted: | 2023-06-01 08:30 |
| Submitted by: | Eccles, Stefan |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We develop a framework based on the covariant phase space formalism that identifies gravitational edge modes as dynamical reference frames. They enable the identification of the associated spacetime region and the imposition of boundary conditions in a gauge-invariant manner. While recent proposals considered the finite region in isolation and sought the maximal symmetry algebra compatible with that perspective, we regard it as a subregion embedded in a global spacetime and study the symmetries consistent with such an embedding. This clarifies that the frame, although appearing as "new" for the subregion, is built out of the field content of the complement. Given a global variational principle, this also permits us to invoke a systematic post-selection procedure, previously used in gauge theory [arXiv:2109.06184], to produce consistent dynamics for a subregion with timelike boundary. Requiring the subregion presymplectic structure to be conserved by the dynamics leads to an essentially unique prescription and unambiguous Hamiltonian charges. Unlike other proposals, this has the advantage that all spacetime diffeomorphisms acting on the subregion remain gauge and integrable, thus generating a first-class constraint algebra. By contrast, diffeomorphisms acting on the frame-dressed spacetime are physical, and those that are parallel to the boundary are integrable. Further restricting to ones preserving the boundary conditions yields an algebra of conserved charges. These record changes in the relation between the region and its complement as measured by frame reorientations. Finally, we explain how the boundary conditions and presymplectic structure can be encoded into boundary actions. While our formalism applies to any generally covariant theory, we illustrate it on general relativity, and conclude with a detailed comparison of our findings to earlier works. [abridged]
Current status:
Reports on this Submission
Strengths
1- Original and innovative work on the relation between dynamical reference frames and the diffeomorphism gauge invariance of general relativity in the presence of space-time boundaries
2- Mathematically clean treatment of the symplectic potential for general relativity in the covariant phase space formalism with boundaries, and of the dressing of observables with reference frames.
3- Self-contained work
4- Contains a thorough comparison with the several other work on the symplectic potential and symmetries of general relativity, with very clear and helpful technical details
Weaknesses
Weaknesses
1- Long, technical paper, insufficiently highlighting important or new features
2- Illustrations are not particularly helpful.
Report
This manuscript presents original and innovative work on the relation between dynamical reference frames and the diffeomorphism gauge invariance of general relativity in the presence of space-time boundaries. In more technical terms, it provides a mathematically clean treatment of the symplectic potential for general relativity in the covariant phase space formalism with boundaries, and of the appropriate dressing of observables with reference frames to make them gauge-invariant. The work is entirely self-contained, though long and technical as a result. It contains a thorough comparison with the several other works on the symplectic potential and symmetries of general relativity, with very clear and helpful technical details. It is clearly meant to become the reference on the subject. It is definitely a paper that deserves to be published and that meets the exceptionality standards of SciPost.
Nevertheless, the presentation of the work could be substantially improved by properly highlighting the important and new features of the formalism, as well as improving the present figures and adding new illustrations (e.g. for eqn (23), (57), (60), (156-157) and so on…) in order to enhance the readability of the manuscript, help the reader through the technicalities and clarifies the physical meaning of the various terms of the derived equations.
In particular, I would suggest to the authors to add to the Conclusion (Section 8) explanations on the appropriate chosen result and equation of the approach (the equation relating the map U and the symplectic potential or the derived charges or what the authors deem to be an essential result of their work), in order to highlight what should definitely be remembered beyond all the technical formalism. Moreover, it would be helpful to also describe what is meant mathematically and physically by “relational map” at the end of the 2nd paragraph in the conclusion.