An algebra of proper observables at null infinity: Dirac brackets, memory and Goldstone probes
- 1Perimeter Institute for Theoretical Physics
- 2Aix Marseille Univ., Univ. de Toulon, CNRS, CPT, UMR 7332
Abstract
We develop a rigorous evaluation of Dirac brackets for classical observables on the phase space of radiative gravitational modes at null infinity that naturally incorporates memory effects. Considering the Ashtekar-Streubel phase space, with boundary conditions in time given by vanishing news and purely electric shear, and taking into account the infinite dimensionality of the phase space, we identify the algebra of proper observables (understood as functions on phase space that can be associated with smooth symplectic flows). We show that the action of supertranslation charges generates the correct transformations on the shear. We also show that the conventional definition of the “Goldstone mode” adopted in the literature cannot be associated with a proper observable, but nevertheless there exists an infinite family of proper observables, which we call Goldstone probes, that are capable of measuring the Goldstone mode. We notice that there are no Goldstone probes constructed only out of the shear or the news, providing a possible explanation for why attempts to construct a (separable) Hilbert space with different memory states have failed so far. Finally, we derive formulas for distributional Dirac brackets between local shear and news, and show that they contain non-local corrections.
Related
- Semiclassical state on algebra of observables for de Sitter space and time reversal symmetry
- A closed formula for the Poisson cohomology of scalar Dubrovin-Novikov brackets in arbitrary dimension
- Gravitational Waves and Nambu-Goldstone Bosons from Infrared-Finite Cosmic Strings
- Discrete differential-geometric Poisson brackets: general theory and explicit constructions
- Nonlinear gauge maps and the structure of Goldstone loops in canonical inflation
BibTeX
@article{silva2026algebra,
title = {{An algebra of proper observables at null infinity: Dirac brackets, memory and Goldstone probes}},
author = {Rodrigo Andrade e Silva and Simone Speziale},
journal = {Journal of High Energy Physics},
year = {2026},
month = nov,
doi = {10.1007/jhep11(2026)066},
url = {https://link.springer.com/article/10.1007/JHEP11(2026)066},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - An algebra of proper observables at null infinity: Dirac brackets, memory and Goldstone probes
AU - Rodrigo Andrade e Silva
AU - Simone Speziale
PY - 2026
DA - 2026/11/06
JO - Journal of High Energy Physics
DO - 10.1007/jhep11(2026)066
UR - https://link.springer.com/article/10.1007/JHEP11(2026)066
AB - We develop a rigorous evaluation of Dirac brackets for classical observables on the phase space of radiative gravitational modes at null infinity that naturally incorporates memory effects. Considering the Ashtekar-Streubel phase space, with boundary conditions in time given by vanishing news and purely electric shear, and taking into account the infinite dimensionality of the phase space, we identify the algebra of proper observables (understood as functions on phase space that can be associated with smooth symplectic flows). We show that the action of supertranslation charges generates the correct transformations on the shear. We also show that the conventional definition of the “Goldstone mode” adopted in the literature cannot be associated with a proper observable, but nevertheless there exists an infinite family of proper observables, which we call Goldstone probes, that are capable of measuring the Goldstone mode. We notice that there are no Goldstone probes constructed only out of the shear or the news, providing a possible explanation for why attempts to construct a (separable) Hilbert space with different memory states have failed so far. Finally, we derive formulas for distributional Dirac brackets between local shear and news, and show that they contain non-local corrections.
SN - 1029-8479
ER -