Quantum Mechanics of a Spherically Symmetric Causal Diamond in Minkowski Spacetime

TL;DR

This paper develops a phase space framework for a spherically symmetric causal diamond in Minkowski spacetime, identifying key charges related to horizon area and size, and explores their quantum properties.

Contribution

It introduces a covariant phase space formalism for causal diamonds, revealing two Iyer-Wald charges and their roles in horizon dynamics and size variation.

Findings

Identification of phase space degrees of freedom localized at the horizon

Derivation of two Iyer-Wald charges, including one related to area and another to size

Quantization of the phase space and analysis of charge properties

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.