Quantum Mechanics of a Spherically Symmetric Causal Diamond in Minkowski Spacetime

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 $d\ge 2$ only if we allow for field-dependent diffeomorphisms and is responsible for changing the size of the causal diamond.

9 pages, 2 figures; v2: Added minor clarifications throughout, version to appear in PRL

References in corpus (11)

• Towards a derivation of holographic entanglement entropy
• Null boundary phase space: slicings, news and memory
• On the Membrane Paradigm and Spontaneous Breaking of Horizon BMS Symmetries
• Near-Horizon BMS Symmetry, Dimensional Reduction, and Black Hole Entropy
• Modular Fluctuations from Shockwave Geometries
• Matrix Quantization of Gravitational Edge Modes
• Quantum Null Geometry and Gravity
• Near-Horizon Quantum Dynamics of 4-d Einstein Gravity from 2-d JT Gravity
• Spontaneously Broken Asymptotic Symmetries and an Effective Action for Horizon Dynamics
• Rindler Fluids from Gravitational Shockwaves
• On the Charge Algebra of Causal Diamonds in Three Dimensional Gravity

Cited by in corpus (6)

• Quantum Area Fluctuations from Gravitational Phase Space
• Modular Fluctuations in Cosmology
• Thermodynamics of a Spherically Symmetric Causal Diamond in Minkowski Spacetime
• Phenomenology of Holography via Quantum Coherence on Causal Horizons
• From Asymptotically Flat Gravity to Finite Causal Diamonds
• Effective density matrix for vacua in asymptotically flat gravity