2006/06/30 by N. Kiriushcheva, S. V. Kuzmin, D. G. C. McKeon · 22 citations
Mathematics · Physics and Astronomy · #Algebra over a field #Black Holes and Theoretical Physics #Constraint algebra #Cosmology and Gravitation Theories #Diffeomorphism #Hamiltonian (control theory) #Hilbert space #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum mechanics #hep-th
paper · pdf · doi:10.1142/s0217751x06029545
published in International Journal of Modern Physics A 21(16), 3401-3420 (World Scientific) · 21 pages, published in Int. J. Mod. Phys. A, Vol. 21, 3401-3420 (2006)
openalex publication_date 2006/06/30 · arxiv created 2006/09/29 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Using the Dirac constraint formalism, we examine the canonical structure of the Einstein–Hilbert action [Formula: see text], treating the metric g αβ and the symmetric affine connection [Formula: see text] as independent variables. For d>2 tertiary constraints naturally arise; if these are all first class, there are d(d-3) independent variables in phase space, the same number that a symmetric tensor gauge field ϕ μν possesses. If d = 2, the Hamiltonian becomes a linear combination of first class constraints obeying an SO (2, 1) algebra. These constraints ensure that there are no independent degrees of freedom. The transformation associated with the first class constraints is not a diffeomorphism when d = 2; it is characterized by a symmetric matrix ξ μν . We also show that the canonical analysis is different if [Formula: see text] is used in place of g αβ as a dynamical variable when d = 2, as in d dimensions, [Formula: see text]. A comparison with the formalism used in the ADM analysis of the Einstein–Hilbert action in first order form is made by applying this approach in the two-dimensional case with h αβ and [Formula: see text] taken to be independent variables.