Related papers: On the Geometric Quantization of Canonical Gravity
We propose a solution to the problem of time for systems with a single global Hamiltonian constraint. Our solution stems from the observation that, for these theories, conventional gauge theory methods fail to capture the full classical…
Ambiguities arising in different approaches (canonical, quasiclassical, path integration) to quantization are discussed by an example of the mechanics of a point-like particle in the Riemannian space (the geodesic dynamics). A way to select…
The Hamiltonian constraint of scalar-tensor theories in the Jordan frame is quantised using three quantisation prescriptions in loop quantum cosmology, from which we obtain three different effective Hamiltonian constraints. The…
In this paper explore the relation between covariant and canonical approaches to quantum gravity and $BF$ theory. We will focus on the dynamical triangulation and spin-foam models, which have in common that they can be defined in terms of…
Standard techniques of canonical gravity quantization on the superspace of 3--metrics are known to cause insurmountable difficulties in the description of time evolution. We forward a new quantization procedure on the superspace of true…
The theory of canonical linearized gravity is quantized using the Projection Operator formalism, in which no gauge or coordinate choices are made. The ADM Hamiltonian is used and the canonical variables and constraints are expanded around a…
Canonical Hamiltonian field theory in curved spacetime is formulated in a manifestly covariant way. Second quantization is achieved invoking a correspondence principle between the Poisson bracket of classical fields and the commutator of…
We consider quantum mechanics on constrained surfaces which have non-Euclidean metrics and variable Gaussian curvature. The old controversy about the ambiguities involving terms in the Hamiltonian of order hbar^2 multiplying the Gaussian…
The degree of freedom of the scalar field in scalar-tensor gravity is employed as "time" to deparametrize the Hamiltonian constraint of the theory. The deparametrized system is then nonperturbatively quantized by the approach of loop…
One method to overcome the notorious problem of time in the quantisation of gravity is the identification of a physically preferred time parameter, a promising candidate being so-called `York time'. The dynamical equations for matter and…
In the last 20 years, loop quantum gravity, a background independent approach to unify general relativity and quantum mechanics, has been widely investigated. The aim of loop quantum gravity is to construct a mathematically rigorous,…
In the model of a fermion field coupled to loop quantum gravity, we consider the Gauss and the Hamiltonian constraints. According to the explicit solutions to the Gauss constraint, the fermion spins and the gravitational spin networks…
We advocate an alternative description of canonical gravity in 3+1 dimensions, obtained by using as the basic variable a real variant of the usual Ashtekar connection variables on the spatial three-manifold. With this ansatz, no non-trivial…
Cosmological perturbation equations are derived systematically in a canonical scheme based on Ashtekar variables. A comparison with the covariant derivation and various subtleties in the calculation and choice of gauges are pointed out.…
The classical theory of gravity predicts its own demise -- singularities. We therefore attempt to quantize gravitation, and present here a new approach to the quantization of gravity wherein the concept of time is derived by imposing the…
Although an important issue in canonical quantization, the problem of representing the constraint algebra in the loop representation of quantum gravity has received little attention. The only explicit computation was performed by Gambini,…
We present a line by line derivation of canonical quantum mechanics stemming from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This viewpoint can…
These notes summarise a talk surveying the combinatorial or Hamiltonian quantisation of three dimensional gravity in the Chern-Simons formulation, with an emphasis on the role of quantum groups and on the way the various physical constants…
Starting with the generally well accepted opinion that quantizing an arbitrary Hamiltonian system involves picking out some additional structure on the classical phase space (the {\sl shadow} of quantum mechanics in the classical theory),…
In the investigation and resolution of the cosmological constant problem the inclusion of the dynamics of quantum gravity can be a crucial step. In this work we suggest that the quantum constraints in a canonical theory of gravity can…