相关论文: Canonical LQG operators and kinematical states for…

This is the first of two papers which study the behavior of the SU(2) holonomies of loop quantum gravity (LQG), when they are acted upon by a unidirectional, plane gravity wave. Initially, the LQG flux-holonomy variables are treated as…

Loop quantum gravity methods are applied to a symmetry-reduced model with homogeneity in two dimensions, derived from a Gowdy model [5,6]. The conditions for propagation of unidirectional plane gravitational waves at exactly the speed of…

This paper constructs an approximate sinusoidal wave packet solution to the equations of loop quantum gravity (LQG). There is an SU(2) holonomy on each edge of the LQG simplex, and the goal is to study the behavior of these holonomies under…

This is the first paper of a series dedicated to LQG coherent states and cosmology. The concept is based on the effective dynamics program of Loop Quantum Cosmology, where the classical dynamics generated by the expectation value of the…

In this thesis we consider the problem of dynamics in canonical loop quantum gravity, primarily in the context of deparametrized models, in which a scalar field is taken as a physical time variable for the dynamics of the gravitational…

Working within the framework of Loop Quantum Gravity (LQG), we construct a set of three operators suitable for identifying coordinate-like quantities on a spin-network configuration. In doing so, we rely on known properties of operators for…

The operator algebraic framework plays an important role in mathematical physics. Many different operator algebras exist for example for a theory of quantum mechanics. In Loop Quantum Gravity only two algebras have been introduced until…

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…

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 use the…

The definition of the Riemann-Cartan space of the plane wave type is given. The condition under which the torsion plane waves exist is found. It is expressed in the form of the restriction imposed on the coupling constants of the…

The algebra of generalized linear quantum canonical transformations is examined in the prespective of Schwinger's unitary-canonical basis. Formulation of the quantum phase problem within the theory of quantum canonical transformations and…

Wave function of a single linear graviton and its interpretation are proposed. The evolution equation for this function is given. A Hermitian operator with mutually commuting components canonically conjugated to the momentum operator of the…

We describe an approach to the quantization of (2+1)--dimensional gravity with topology R x T^2 and negative cosmological constant, which uses two quantum holonomy matrices satisfying a q--commutation relation. Solutions of diagonal and…

The philosophy of the Loop Quantum Gravity approach is to construct the canonical variables by using the duality of infinitesimal connections and holonomies along loops. Based on this fundamental property for example the holonomy-flux…

We present a new method for constructing operators in loop quantum gravity. The construction is an application of the general idea of "coherent state quantization", which allows one to associate a unique quantum operator to every function…

As part of a wider study of coherent states in (loop) quantum gravity, we introduce a modification to the standard construction, based on the recently introduced (non-commutative) flux representation. The resulting quantum states have some…

An algebraic formulation of general relativity is proposed. The formulation is applicable to quantum gravity and noncommutative space. To investigate quantum gravity we develop the canonical formalism of operator geometry, after…

We treat the canonical commutation relations and the conventional calculus based on it as an algebraic syntax of quantum mechanics and establish a geometric semantics of this syntax. This leads us to a geometric model, the space of states…

The canonical analysis and subsequent quantization of the (2+1)-dimensional action of pure gravity plus a cosmological constant term is considered, under the assumption of the existence of one spacelike Killing vector field. The proper…

We present a separable version of Loop Quantum Gravity (LQG) based on an inductive system of cubic lattices. We construct semi-classical states for which the LQG operators -- the flux, the area and the volume operators -- have the right…