Quantum Mechanics of a Spherically Symmetric Causal Diamond in Minkowski Spacetime
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1.
California Institute of Technology
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2.
University of Amsterdam
Abstract
We construct the phase space of a spherically symmetric causal diamond in (d+2)-dimensional Minkowski spacetime. Utilizing the covariant phase space formalism, we identify the relevant degrees of freedom that localize to the d-dimensional bifurcate horizon and, upon canonical quantization, determine their commutators. On this phase space, we find two Iyer-Wald charges. The first of these charges, proportional to the area of the causal diamond, is responsible for shifting the null time along the horizon and has been well documented in the literature. The second charge is much less understood, being integrable for d≥2 only if we allow for field-dependent diffeomorphisms and is responsible for changing the size of the causal diamond.
Copyright and License
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.
Acknowledgement
We would like to thank Luca Ciambelli, Laura Donnay, Laurent Freidel, Antony Speranza, and Céline Zwikel for useful discussions. M. B., T. H., Y. Z., and K. Z. are supported by the Heising-Simons Foundation “Observational Signatures of Quantum Gravity” collaboration Grant No. 2021-2817, the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and the Walter Burke Institute for Theoretical Physics. M. B., Y. Z., and K. Z. are also supported by GQuEST funding provided from the U.S. Department of Energy via FNAL: DE-AC02-07CH11359. M. B. acknowledges the support of the Natural Sciences and Engineering Research Council of Canada (NSERC) [Funding Reference No. PGS D—578032–2023]. P. M. is supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 852386). The work of K. Z. is also supported by a Simons Investigator Award.
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Additional details
Related works
- Is new version of
- Discussion Paper: arXiv:2408.11094 (arXiv)
Funding
- Heising-Simons Foundation
- 2021-2817
- United States Department of Energy
- DE-SC0011632
- Walter Burke Institute for Theoretical Physics
- United States Department of Energy
- DE-AC02-07CH11359
- Natural Sciences and Engineering Research Council
- PGS D—578032–2023
- European Research Council
- European Commission
- 852386
- Simons Foundation
- SCOAP3
Dates
- Accepted
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2025-03-12