Quantum Mechanics of a Spherically Symmetric Causal Diamond in Minkowski Spacetime
Mathew W. Bub (Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA); Temple He (Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA); Prahar Mitra (Institute for Theoretical Physics, University of Amsterdam, Science Park 904, Postbus 94485, 1090 GL Amsterdam, The Netherlands); Yiwen Zhang (Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA); Kathryn M. Zurek (Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA)
We construct the phase space of a spherically symmetric causal diamond in ()-dimensional Minkowski spacetime. Utilizing the covariant phase space formalism, we identify the relevant degrees of freedom that localize to the -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 only if we allow for field-dependent diffeomorphisms and is responsible for changing the size of the causal diamond.
