Algebraic analysis of a model of two-dimensional gravity

2009/01/31 by A. M. Frolov, N. Kiriushcheva, S. V. Kuzmin
Mathematics · Physics and Astronomy · #Algebraic number #Black Holes and Theoretical Physics #Constraint algebra #Covariant Hamiltonian field theory #Differential geometry #Eigenvalues and eigenvectors #Hamiltonian (control theory) #Homotopy and Cohomology in Algebraic Topology #Noncommutative and Quantum Gravity Theories #Poisson algebra #Poisson bracket #Poisson distribution #Superintegrable Hamiltonian system #hep-th

paper · pdf · doi:10.1007/s10714-010-0935-2

published as Gen.Rel.Grav.42:1649-1666,2010 · 21 pages, to appear in General Relativity and Gravitation

arxiv created 2010/02/04 · openalex publication_date 2010/02/10 · arxiv updated 2014/11/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

An algebraic analysis of the Hamiltonian formulation of the model two-dimensional gravity is performed. The crucial fact is an exact coincidence of the Poisson brackets algebra of the secondary constraints of this Hamiltonian formulation with the SO(2,1)-algebra. The eigenvectors of the canonical Hamiltonian H_c are obtained and explicitly written in closed form.

Citations

• Irreducible Unitary Representations of the Lorentz Group
• Deduzione invariantiva delle equazioni gravitazionali dal principio di Hamilton
• Dirac and Lagrangian reductions in the canonical approach to the first-order form of the Einstein–Hilbert action