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Quantum Mechanics of a Spherically Symmetric Causal Diamond in Minkowski Spacetime
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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 $d \geq 2$ only if we allow for field-dependent diffeomorphisms and is responsible for changing the size of the causal diamond.
Forward citations
Cited by 4 Pith papers
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From Asymptotically Flat Gravity to Finite Causal Diamonds
The soft sector phase space of asymptotically flat gravity equals the phase space of radial size fluctuations of a finite causal diamond in flat spacetime.
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Surg-InvNeRF: Invertible NeRF for 3D tracking and reconstruction in surgical vision
An invertible-NeRF test-time optimization approach tracks points in 2D and 3D across surgical videos, reporting roughly 50% higher average precision than prior optimization-based 2D trackers.
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Foundational Structure of Local Amplitudes in Quantum Gravity
Local amplitudes for causal diamonds can be constructed from null-slab boundary states, projectors, and vacuum intertwiners, with Ward identities and charge conservation as consequences.
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Effective density matrix for vacua in asymptotically flat gravity
The vacuum of a large causal diamond in asymptotically flat gravity is claimed to be a Gaussian in the supertranslation Goldstone mode, giving modular Hamiltonian variance A/epsilon squared.
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