Related papers: New representation and a vacuum state for canonica…
We study the algebra of constraints of quantum gravity in the loop representation based on Ashtekar's new variables. We show by direct computation that the quantum commutator algebra reproduces the classical Poisson bracket one, in the…
In its canonical formulation, general relativity is subject to gauge transformations that are equivalent to space-time coordinate changes of general covariance only when the gauge generators, given by the Hamiltonian and diffeomorphism…
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…
Canonical methods allow the derivation of effective gravitational actions from the behavior of space-time deformations reflecting general covariance. With quantum effects, the deformations and correspondingly the effective actions change,…
The Wilson loop functionals in terms of Ashtekar's variables were the first (formal) solutions to the quantized hamiltonian constraint of canonical gravity. Here it is shown that the same functionals also solve the supergravity constraints…
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…
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…
Any canonical quantum theory can be understood to arise from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This geometric perspective offers a…
First, we describe the construction of a new type of gravity-matter models based on the formalism of non-Riemannian space-time volume forms - alternative generally covariant integration measure densities (volume elements) defined in terms…
As a canonical and generally covariant gauge theory, loop quantum gravity requires special techniques to derive effective actions or equations. If the proper constructions are taken into account, the theory, in spite of considerable…
New results from the new variables/loop representation program of nonperturbative quantum gravity are presented, with a focus on results of Ashtekar, Rovelli and the author which greatly clarify the physical interpretation of the quantum…
We present a systematic expansion of all constraint equations in canonical quantum gravity up to the order of the inverse Planck mass squared. It is demonstrated that this method generates the conventional Feynman diagrammatic technique…
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…
Quantum gravity places entirely new challenges on the formulation of a consistent theory as well as on an extraction of potentially observable effects. Quantum corrections due to the gravitational field are commonly expected to be tiny…
In this paper the quantization of the 2$+$1-dimensional gravity couplet to the massless Dirac field is carried out. The problem is solved by the application of the new Dynamic Quantization Method [1,2]. It is well-known that in general…
The quantum potential approach makes it possible to construct a complementary picture of quantum mechanical evolution which reminds classical equation of motion. The only difference as compared to equations of motion for the underlying…
The ADM approach to canonical general relativity combined with Dirac's method of quantizing constrained systems leads to the Wheeler-DeWitt equation. A number of mathematical as well as physical difficulties that arise in connection with…
Loop Quantum Gravity (LQG) is a promising approach to quantum gravity, in particular because it is based on a rigorous quantization of the kinematics of gravity. A difficult and still open problem in the LQG program is the construction of…
The flat, homogeneous, and isotropic universe with a massless scalar field is a paradigmatic model in Loop Quantum Cosmology. In spite of the prominent role that the model has played in the development of this branch of physics, there still…
We discuss the canonical treatment and quantization of matter coupled supergravity in three dimensions, with special emphasis on $N=2$ supergravity. We then analyze the quantum constraint algebra; certain operator ordering ambiguities are…