Related papers: Hamiltonian Approach To 2+1 Dimensional Gravity
In asymptotically anti-de Sitter gravity, diffeomorphisms that change the conformal boundary data can be promoted to genuine physical degrees of freedom. I show that in 2+1 dimensions, the dynamics of these degrees of freedom is described…
Non-abelian higher gauge theory has recently emerged as a generalization of standard gauge theory to higher dimensional (2-dimensional in the present context) connection forms, and as such, it has been successfully applied to the…
We discuss the Dirac quantization of two dimensional gravity with bosonic matter fields. After defining the extended Hamiltonian it is possible to fix the gauge completely. The commutators can all be obtained in closed form; nevertheless,…
In this contribution we sketch a branch-cut quantum formulation of the Wheeler-DeWitt equation analytically continued to the complex plane. As a starting point, we base our approach on the Ho\v{r}ava-Lifshitz formulation of gravity, which…
The quantization of the induced 2d-gravity on a compact spatial section is carried out in three different ways. In the three approaches the supermomentum constraint is solved at the classical level but they differ in the way the hamiltonian…
The canonical Hamiltonian $H_C$ of the metric General Relativity is reduced to its natural form. The natural form of canonical Hamiltonian provides numerous advantages in actual applications to the metric GR, since the general theory of…
A path integral evaluation of the Green's function for the hydrogen atom initiated by Duru and Kleinert is studied by recognizing it as a special case of the general treatment of the separable Hamiltonian of Liouville-type. The basic…
By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form by using a…
Taking (2+1)-dimensional pure Einstein gravity for arbitrary genus $g$ as a model, we investigate the relation between the partition function formally defined on the entire phase space and the one written in terms of the reduced phase…
We analyse general form of theory with the dynamical determinant of metric. We show that due to the presence of general function of determinant that multiplies scalar curvature Hamiltonian constraint is either second class constraint or it…
The Hamiltonian approach to General Relativity is developed similarly to the Wheeler-DeWitt Hamiltonian cosmology, where the cosmological scale factor is treated as a time-like dynamic variable and its canonical momentum is considered as an…
The Hamiltonian dynamics of \(2 + 1\) dimensional Yang-Mills theory with gauge group SU(2) is reformulated in gauge invariant, geometric variables, as in earlier work on the \(3 + 1\) dimensional case. Physical states in electric field…
The so called "New Massive Gravity" in $D=2+1$ consists of the Einstein-Hilbert action (with minus sign) plus a quadratic term in curvatures ($K$-term). Here we perform the Kaluza-Klein dimensional reduction of the linearized $K$-term to…
A covariant Hamiltonian description of Palatini's gravity on manifolds with boundary is presented. Palatini's gravity appears as a gauge theory satisfying a constraint in a certain topological limit. This approach allows the consideration…
We solve Einstein's equations with negative cosmological constant in $2+1$ dimensions in the Hamiltonian formulation. The spacetime has the topology of $\Sigma \times \mathbf{R}$ where $\mathbf{R}$ corresponds to the time direction and…
We construct the generator of hamiltonian gauge symmetries in a 2+1 dimensional massive theory of gravity, proposed recently, through a systematic off-shell algorithm. Using a field dependant map among gauge parameters we show that the…
The Hamiltonian constraint Hc = NH = 0, defines a diffeomorphic structure on spatial manifolds by the lapse function N in general theory of relativity. However, it is not manifest in Lanczos-Lovelock gravity, since the expression for…
The Hamiltonian formalism of the generalized unimodular gravity theory, which was recently suggested as a model of dark energy, is shown to be a complicated example of constrained dynamical system. The set of its canonical constraints has a…
The reduction of the dreibein formalism of 2+1 General Relativity to the holonomies is explicitly performed. We also show explicitly how to relate these holonomies to a geometry classically, and how to generate these holonomies from any…
The 3+1 (canonical) decomposition of all geometries admitting two-dimensional space-like surfaces is exhibited. A proposal consisting of a specific re-normalization {\bf Assumption} and an accompanying {\bf Requirement} is put forward,…