Related papers: Hamiltonian Theory: Dynamics
We describe our recent proposal of a path integral formulation of classical Hamiltonian dynamics. Which leads us here to a new attempt at hybrid dynamics, which concerns the direct coupling of classical and quantum mechanical degrees of…
The implementation of the dynamics in loop quantum gravity (LQG) is still an open problem. Here, we discuss a tentative dynamics for the simplest class of graphs in LQG: Two vertices linked with an arbitrary number of edges. We find an…
We present a generalization of the first-order formalism used to describe the dynamics of a classical system. The generalization is then applied to the first-order action that describes General Relativity. As a result we obtain equations…
Connecting ideas of geometric formulation of quantum mechanics with new results in symplectic geometry a new approach to geometrical quantization procedure is proposed. As a first result we verify that the correspondence between "classical"…
It is discussed a truncation of the kinematical Hilbert space of Loop Quantum Gravity, which describes the dynamical system associated with an inhomogeneous cosmological model.
General aspects of vielbein representation, ADM formulation and canonical quantization of gravity are reviewed using pure gravity in three dimensions as a toy model. The classical part focusses on the role of observers in general…
We discuss the semiclassical limit of Quantum Reduced Loop Gravity, a recently proposed model to address the quantum dynamics of the early Universe. We apply the techniques developed in full Loop Quantum Gravity to define the semiclassical…
In this paper, a version of polymer quantum mechanics, which is inspired by loop quantum gravity, is considered and shown to be equivalent, in a precise sense, to the standard, experimentally tested, Schroedinger quantum mechanics. The…
We generalize the Hamiltonian picture of General Relativity coupled to classical matter, known as geometrodynamics, to the case where such matter is described by a Quantum Field Theory in Curved Spacetime, but gravity is still described by…
The loop quantization of Brans-Dicke theory (with coupling parameter $\omega\neq-3/2$) is studied. In the geometry-dynamical formalism, the canonical structure and constraint algebra of this theory are similar to those of general relativity…
Quantum geometrodynamics is canonical quantum gravity with the three-metric as the configuration variable. Its central equation is the Wheeler--DeWitt equation. Here I give an overview of the status of this approach. The issues discussed…
Loop Quantum Gravity (LQG) is one of the leading approaches to unify quantum physics and General Relativity (GR). The Hilbert space of LQG is spanned by spin-networks which describe the local geometry of quantum space-time. Simulation of…
The talk is devoted to the "extended phase space" approach to Quantum Geometrodynamics. The premises that have led to the formulation of this approach are briefly reviewed, namely, non-trivial topology of the Universe which implies the…
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…
We present a new reformulation of the canonical quantum geometrodynamics, which allows to overcome the fundamental problem of the frozen formalism and, therefore, to construct an appropriate Hilbert space associate to the solution of the…
We present a non-perturbative quantization of general relativity coupled to dust and other matter fields. The dust provides a natural time variable, leading to a physical Hamiltonian with spatial diffeomorphism symmetry. The methods of loop…
We compute explicitly the equations of motion of the Hamiltonian formulation of quadratic gravity. This is the theory with the most general Lagrangian with terms of quadratic order in the curvature tensor. We employ the symbolic…
The goal of this contribution is to introduce the Hamiltonian formalism of theoretical mechanics for analysing motion in generic linear and non-linear dynamical systems, including particle accelerators. This framework allows the derivation…
The appearance of Hamiltonian constraint in the canonical formalism for general relativity reflects the lack of a fixed external time. The dynamics of general relativistic systems can be expressed with respect to an arbitrarily chosen…
Canonical quantum gravity provides insights into the quantum dynamics as well as quantum geometry of space-time by its implications for constraints. Loop quantum gravity in particular requires specific corrections due to its quantization…