Equivalent quantisations of (2+1)-dimensional gravity

1993/11/05 by S. Carlip, J. E. Nelson, J.E. Nelson · 2 citations
Physics and Astronomy · #Action (physics) #Black Holes and Theoretical Physics #Constant (computer programming) #Constant curvature #Cosmological constant #Cosmology and Gravitation Theories #Curvature #Effective action #Holonomy #Moduli #Noncommutative and Quantum Gravity Theories #gr-qc #hep-th

paper · pdf · doi:10.1016/0370-2693(94)90197-x

published as Phys.Lett.B324:299-302,1994 · 7 pages, Plain Tex, DFTT 67/93, UCD-93-33

arxiv created 1993/11/05 · openalex publication_date 1994/04/01 · arxiv updated 2010/04/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

For spacetimes with the topology \IR × T², the action of (2+1)-dimensional gravity with negative cosmological constant \La is written uniquely in terms of the time-independent traces of holonomies around two intersecting noncontractible paths on T². The holonomy parameters are related to the moduli on slices of constant mean curvature by a time-dependent canonical transformation which introduces an effective Hamiltonian. The quantisation of the two classically equivalent formulations differs by terms of order O(ℏ³), negligible for small |\La|.

Citations

• Modular group, operator ordering, and time in (2+1)-dimensional gravity
• Invariants of 2+1 gravity
• 2 + 1 dimensional gravity as an exactly soluble system

Cited by

• Quantum modular group in (2+1)-dimensional gravity
• Comparative quantizations of (2+1)-dimensional gravity