Related papers: Holonomy operator for spin connection and spatial …

It is shown that the Riemannian curvature of the 3-dimensional hypersurfaces in space-time, described by the Wilson loop integral, can be represented by a quaternion quantum operator induced by the SU(2) gauge potential, thus providing a…

(This is a report for the Proceedings of ``Journees Relativistes 1993'' written in September 1993. Containes a short description of the results published elsewhere in the joint paper with A. Ashtekar) Integral calculus on the space of gauge…

Recently, a new class of scalar constraint operators has been introduced in loop quantum gravity. They are defined on a space of solutions to the Gauss constraint and partial solutions to the vector constraint, called a vertex Hilbert…

Any field, even if it lives in a completely hidden sector, interacts with the visible sector at least via the gravitational interaction. In this paper, we show that a scalar field in such a hidden sector generically couples to the quadratic…

We introduce simple generic models of surface dynamics in loop quantum gravity (LQG). A quantum surface is defined as a set of elementary patches of area glued together. We provide it with an extra structure of locality (nearest neighbors),…

In this paper, we construct the phase space of a constantly curved tetrahedron with fixed triangle areas in terms of a pair of Darboux coordinates called the length and twist coordinates, which are in analogy to the Fenchel-Nielsen…

We extend the formalism of embedded spin networks and spin foams to include topological data that encode the underlying three-manifold or four-manifold as a branched cover. These data are expressed as monodromies, in a way similar to the…

Two sets of spatially diffeomorphism invariant operators are constructed in the loop representation formulation of quantum gravity. This is done by coupling general relativity to an anti- symmetric tensor gauge field and using that field to…

Holonomic Quantum Computation (HQC) is an all-geometrical approach to quantum information processing. In the HQC strategy information is encoded in degenerate eigen-spaces of a parametric family of Hamiltonians. The computational network of…

We show that holography arises naturally in the context of spherically symmetric loop quantum gravity. The result is not dependent on detailed assumptions about the dynamics of the theory being considered. It ties strongly the amount of…

New universal invariant operators are introduced in a class of geometries which include the quaternionic structures and their generalisations as well as 4-dimensional conformal (spin) geometries. It is shown that, in a broad sense, all…

We show that the principal part of the Dirac Hamiltonian in 3+1 dimensions emerges in a semi-classical approximation from a construction which encodes the kinematics of quantum gravity. The construction is a spectral triple over a…

In this paper we show that via the configuration space integral construction a non-trivalent graph cocycle can also yield a non-zero cohomology class of the space of higher (and even) codimensional long knots. This simultaneously proves…

Families of conformal field theories are naturally endowed with a Riemannian geometry which is locally encoded by correlation functions of exactly marginal operators. We show that the curvature of such conformal manifolds can be computed…

We propose a new holonomy formulation for spin foams, which naturally extends the theory space of lattice gauge theories. This allows current spin foam models to be defined on arbitrary two-complexes as well as to generalize current spin…

We recently introduced a new representation for loop quantum gravity, which is based on the BF vacuum and is in this sense much nearer to the spirit of spin foam dynamics. In the present paper we lay out the classical framework underlying…

To understand the dynamics of loop quantum gravity, the deparametrized model of gravity coupled to a scalar field is studied in a simple case, where the graph underlying the spin network basis is one loop based at a single vertex. The…

We argue that the holographic formula relating entanglement entropy and the area of a minimal surface is the key to define the area of surfaces in the (emergent) spacetime from the dual theory on the boundary. So we promote the entropy/area…

Within the twistorial parametrization of Loop Quantum Gravity we investigate the consequences of choosing a spacelike normal vector in the linear simplicity constraints. The amplitudes for the $SU(2)$ boundary states of Loop Quantum…

In this paper we discuss propagation of the weak high-frequency gravitational waves in a curved spacetime background. We develop a so-called spinoptics approximation which takes into account interaction of the spin of the field with the…