1996/05/01 by T. Ohta, Tadayuki Ohta, R. B. Mann +1 · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Canonical coordinates #Canonical quantization #Cosmology and Gravitation Theories #Covariant Hamiltonian field theory #Gravitation #Gravitational field #Hamiltonian (control theory) #Hamiltonian formalism #Noncommutative and Quantum Gravity Theories #Scalar field #f(R) gravity #gr-qc
paper · pdf · doi:10.1088/0264-9381/13/9/022
published as Class.Quant.Grav. 13 (1996) 2585-2602 · 21 pages, latex
arxiv created 1996/05/01 · openalex publication_date 1996/09/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We develop the formalism for canonical reduction of (1 + 1)-dimensional gravity coupled with a set of point particles by eliminating constraints and imposing coordinate conditions. The formalism itself is quite analogous to the (3 + 1)-dimensional case; however in (1 + 1) dimensions an auxiliary scalar field is shown to have an important role. The reduced Hamiltonian is expressed as a form of spatial integral of the second derivative of the scalar field. Since in (1 + 1) dimensions there exists no dynamical degree of freedom of the gravitational field (i.e. the transverse-traceless part of the metric tensor is zero), the reduced Hamiltonian is completely determined in terms of the particles' canonical variables (coordinates and momenta). The explicit form of the Hamiltonian is calculated both in post-linear and post-Newtonian approximations.