Related papers: The Diffeomorphism Constraint Operator in Loop Qua…

This work introduces a new space $\T'_*$ of `vertex-smooth' states for use in the loop approach to quantum gravity. Such states provide a natural domain for Euclidean Hamiltonian constraint operators of the type introduced by Thiemann (and…

The G -->0 limit of Euclidean gravity introduced by Smolin is described by a generally covariant U(1)xU(1)xU(1) gauge theory. The Poisson bracket algebra of its Hamiltonian and diffeomorphism constraints is isomorphic to that of gravity.…

Classical gravitational evolution admits an elegant and compact re-expression in terms of gauge covariant generalizations of Lie derivatives with respect to a spatial phase space dependent $su(2)$ valued vector field called the Electric…

We derive a closed formula for the matrix elements of the volume operator for canonical Lorentzian quantum gravity in four spacetime dimensions in the continuum in a spin-network basis. We also display a new technique of regularization…

We analyze the classical limit of kinematic loop quantum gravity in which the diffeomorphism and hamiltonian constraints are ignored. We show that there are no quantum states in which the primary variables of the loop approach, namely the…

We use the method of embedding a subsystem (i.e. its observable algebra) into a larger quantum system to extract a cosmological sector from full Loop Quantum Gravity. The application of this method provides a setting for a systematic study…

We analyze the spectral properties of the volume operator of Ashtekar and Lewandowski in Loop Quantum Gravity, which is the quantum analogue of the classical volume expression for regions in three dimensional Riemannian space. Our analysis…

This paper establishes a link between Noncommutative Geometry and canonical quantum gravity. A semi-finite spectral triple over a space of connections is presented. The triple involves an algebra of holonomy loops and a Dirac type operator…

The G-->0 limit of Euclidean gravity introduced by Smolin is described by a generally covariant U(1)xU(1)xU(1) gauge theory. In an earlier paper, Tomlin and Varadarajan constructed the quantum Hamiltonian constraint of density weight 4/3…

The construction of a continuum limit for the dynamics of loop quantum gravity is unavoidable to complete the theory. We explain that such a construction is equivalent to obtaining the continuum physical Hilbert space, which encodes the…

The fundamental laws of physics can be derived from the requirement of invariance under suitable classes of transformations on the one hand, and from the need for a well-posed mathematical theory on the other hand. As a part of this…

In this review, the fundamental structure of loop quantum gravity is presented pedagogically. Our main aim is to help non-experts to understand the motivations, basic structures, as well as general results. It may also be beneficial to…

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 study the issue of the recovery of diffeomorphism invariance in the recently introduced loop quantum gravity treatment of the exterior Schwarzschild space-time. Although the loop quantization agrees with the quantization in terms of…

The quantum analogue of general relativistic geometry should be implementable on smooth manifolds without an a priori metric structure, the kinematical covariance group acting by diffeomorphisms. Here I approach quantum gravity (QG) in the…

Using the complex-valued self-dual connection variables, the loop quantum cosmology of a closed Friedmann universe coupled to a massless scalar field is studied. It is shown how the reality conditions can be imposed in the quantum theory by…

In a seminal paper, Kaminski, Kisielowski an Lewandowski for the first time extended the definition of spin foam models to arbitrary boundary graphs. This is a prerequisite in order to make contact to the canonical formulation of Loop…

We construct Carrollian scalar field theories in general dimensions, mainly focusing on the boundaries of Minkowski and Rindler spacetime, whose quantum flux operators form a faithful representation of Carrollian diffeomorphism up to a…

In [arXiv:1411.3592] an extension of the Ashtekar-Lewandowski (AL) state space of Loop Quantum Gravity was set up with the help a projective formalism introduced by Kijowski [Kijowski 1977; see also: arXiv:1304.6330, arXiv:1411.3590]. The…

We construct and study Loop Quantum Cosmology (LQC) when the Barbero-Immirzi parameter takes the complex value $\gamma=\pm i$. We refer to this new quantum cosmology as complex Loop Quantum Cosmology. We proceed in making an analytic…