Comparative quantizations of (2+1)-dimensional gravity

1994/11/12 by S. Carlip, Steven Carlip, J. E. Nelson · 3 citations
Mathematics · Physics and Astronomy · #Algebra over a field #Algorithm #Black Holes and Theoretical Physics #Computer science #Cosmological constant #Cosmology and Gravitation Theories #Holonomy #Loop quantum gravity #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Phase space #Physics #Pure mathematics #Quantization (signal processing) #Quantum #Quantum gravity #Quantum mechanics #Slicing #Theoretical physics #gr-qc #hep-th

paper · pdf · doi:10.1103/physrevd.51.5643

published as Phys.Rev.D51:5643-5653,1995 · 24 pages, LaTeX, no figures

arxiv created 1994/11/12 · openalex publication_date 1995/05/15 · arxiv updated 2010/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We compare three approaches to the quantization of (2+1)-dimensional gravity with a negative cosmological constant: reduced phase-space quantization with the York time slicing, quantization of the algebra of holonomies, and quantization of the space of classical solutions. The relationships among these quantum theories allow us to define and interpret time-dependent operators in the ``frozen time'' holonomy formulation.

Citations

• Modular group, operator ordering, and time in (2+1)-dimensional gravity
• Invariants of 2+1 gravity
• Equivalent quantisations of (2+1)-dimensional gravity
• 2 + 1 dimensional gravity as an exactly soluble system
• Time in quantum gravity: An hypothesis

Cited by

• Spacetime singularities in (2 1)-dimensional quantum gravity
• Quantum aspects of 2+1 gravity
• Quantum modular group in (2+1)-dimensional gravity