Quantum Mechanics of a Spherically Symmetric Causal Diamond in Minkowski Spacetime

Understand

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.