Related papers: Quantum Geometry II : The Mathematics of Loop Quan…
The questions I have been asked during the 5th International School on Field Theory and Gravitation, have compelled me to give an account of the premises that I consider important for a beginner's approach to Loop Quantum Gravity. After a…
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…
The geometrical nature of gravity emerges from the universality dictated by the equivalence principle. In the usual formulation of General Relativity, the geometrisation of the gravitational interaction is performed in terms of the…
Loop quantum cosmology(LQC) is the symmetric model of loop quantum gravity. In this paper, we generalize the structure of loop quantum cosmology to the theories with arbitrary spacetime dimensions. The isotropic and homogenous cosmological…
A discussion of the meaning of a physical concept cannot be separated from discussion of the conditions for its ideal measurement. We assert that quantization is no more than the invocation of the quantum of action in the explanation of…
A new framework of loop quantization that assimilates conformal and scale invariance is constructed and is found to be applicable to a large class of physically important theories of gravity and gravity-matter systems. They include general…
Recently, it is shown that, the quantum effects of matter are well described by the conformal degree of freedom of the space-time metric. On the other hand, it is a wellknown fact that according to Einstein's gravity theory, gravity and…
In Loop Quantum Gravity mathematically rigorous models of full quantum gravity were proposed. In this paper we study a cosmological sector of one of the models describing quantum gravity with positive cosmological constant coupled to…
In three spacetime dimensions, general relativity drastically simplifies, becoming a ``topological'' theory with no propagating local degrees of freedom. Nevertheless, many of the difficult conceptual problems of quantizing gravity are…
Quantum Reduced Loop Gravity is a promising framework for linking Loop Quantum Gravity and the effective semiclassical dynamics of Loop Quantum Cosmology. We review its basic achievements and its main perspectives, outlining how it provides…
One can try to define the theory of quantum gravity as the sum over geometries. In two dimensions the sum over {\it Euclidean} geometries can be performed constructively by the method of {\it dynamical triangulations}. One can define a {\it…
A set of diverse but mutually consistent results obtained in different settings has spawned a new view of loop quantum gravity and its physical implications, based on the interplay of operator calculations and effective theory: Quantum…
A quantum physical projector is proposed for generally covariant theories which are derivable from a Lagrangian. The projector is the quantum analogue of the integral over the generators of finite one-parameter subgroups of the gauge…
The geometry of Quantum Mechanics in the context of uncertainty and complementarity, and probability is explored. We extend the discussion of geometry of uncertainty relations in wider perspective. Also, we discuss the geometry of…
We use the mathematical framework of loop quantum gravity (LQG) to study the quantization of three dimensional (Riemannian) gravity with positive cosmological constant (Lambda>0). We show that the usual regularization techniques (successful…
The quantum gravity is formulated based on principle of local gauge invariance. The model discussed in this paper has local gravitational gauge symmetry and gravitational field appears as gauge field. The problems on quantization and…
Quantum gravity is the missing piece in our understanding of the fundamental interactions today. Given recent observational breakthroughs in gravity, providing a quantum theory for what lies beyond general relativity is more urgent than…
Since the early days of search for a quantum theory of gravity the attempts have been mostly concentrated on the quantization of an otherwise classical system. The two most contentious candidate theories of gravity, sting theory and quantum…
We propose a "guide" towards quantisation of gravity based on quantum matter in a statistical mechanics context. On one hand, a statistical mechanics model naturally arises from the thermodynamic interpretation of horizons in Rindler space.…
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…