2023/10/04 by Rodrigo Andrade e Silva, Silva, Rodrigo Andrade e
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Quantum Electrodynamics and Casimir Effect
paper · pdf · doi:10.48550/arxiv.2310.03100
openalex publication_date 2023/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We develop the non-perturbative reduced phase space quantization of causal diamonds in (2+1)-dimensional gravity with a nonpositive cosmological constant. In Part I we described the classical reduction process and the reduced phase space, \widetilde\mathcal P = T^*(Diff+ (S1)/PSL(2, \mathbb R)), while in Part II we discuss the quantization of the phase space and quantum aspects of the causal diamonds. Because the phase space does not have a natural linear structure, a generalization of the standard canonical (coordinate) quantization is required. In particular, as the configuration space is a homogeneous space for the Diff+ (S1) group, we apply Isham's group-theoretic quantization scheme. We propose a quantization based on (projective) unitary irreducible representations of the BMS3 group, which is obtained from a natural prescription for extending Diff+ (S1) into a transitive group of symplectic symmetries of the phase space. We find a class of suitable quantum theories labelled by a choice of a coadjoint orbit of the Virasoro group and an irreducible unitary representation of the corresponding little group. The most natural choice, justified by a Casimir matching principle, corresponds to a Hilbert space realized by wavefunctions on Diff+ (S1)/PSL(2, \mathbb R) valued in some unitary irreducible representation of SL(2, \mathbb R). A surprising result is that the twist of the diamond corner loop is quantized in terms of the ratio of the Planck length to the corner perimeter.