Related papers: Topspin Networks in Loop Quantum Gravity

The problem of finding the quantum theory of the gravitational field, and thus understanding what is quantum spacetime, is still open. One of the most active of the current approaches is loop quantum gravity. Loop quantum gravity is a…

In the context of quantum gravity, we clarify entanglement calculations on spin networks: we distinguish the gauge-invariant entanglement between intertwiners located at the nodes and the entanglement between spin states located on the…

We explore the classical setting for the U(N) framework for SU(2) intertwiners for loop quantum gravity (LQG) and describe the corresponding phase space in terms of spinors with appropriate constraints. We show how its quantization leads…

This article is an extended version of the peer-reviewed publication; Moffat and Wang, J Phys Math 2018, 9:4 DOI: 10.4172/2090-0902.1000289 The article sets out to address a number of issues concerning Loop Quantum Gravity raised by…

In the context of a canonical quantization of general relativity, one can deform the loop gravity phase space on a graph by replacing the T*SU(2) phase space attached to each edge by SL(2,C) seen as a phase space. This deformation is…

We develop a worldline approach to quantum gravity in D=4. Using the background field method we consider the covariantly gauge fixed Einstein-Hilbert action with cosmological constant, and find a worldline representation of the differential…

The purpose of this contribution is to give an introduction to quantum geometry and loop quantum gravity for a wide audience of both physicists and mathematicians. From a physical point of view the emphasis will be on conceptual issues…

We give a standard introduction to loop quantum gravity, from the ADM variables to spin network states. We include a discussion on quantum geometry on a fixed graph and its relation to a discrete approximation of general relativity.

Tensor networks are often used to accurately represent ground states of quantum spin chains. Two popular choices of such tensor network representations can be seen to implement linear maps that correspond, respectively, to euclidean time…

In loop quantum gravity we now have a clear picture of the quantum geometry of space, thanks in part to the theory of spin networks. The concept of `spin foam' is intended to serve as a similar picture for the quantum geometry of spacetime.…

We introduce a new topological effect involving interference of two meson loops, manifesting a path-independent topological area dependence. The effect also draws a connection between quark confinement, Wilson-loops and topological…

Loop quantum gravity is a mature theory. To proceed to explicit calculations in cosmology, it is necessary to make assumptions and simplifications based on the symmetries of the cosmological setting. Symmetry reduction is especially…

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…

We elaborate the idea of quantum computation through measuring the correlation of a gapped ground state, while the bulk Hamiltonian is utilized to stabilize the resource. A simple computational primitive, by pulling out a single spin…

The physics of quantum gravity is discussed within the framework of topological quantum field theory. Some of the principles are illustrated with examples taken from theories in which space-time is three dimensional.

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…

Tensor networks provide a powerful tool for studying many-body quantum systems, particularly making quantum simulations more efficient. In this article, we construct a tensor network representation of the spin network states, which…

We propose a theory for coupling matter fields with discrete geometry on higher-order networks, i.e. cell complexes. The key idea of the approach is to associate to a higher-order network the quantum entropy of its metric. Specifically we…

The Hamiltonian of a gravitational system defined in a region with boundary is quantized. The classical Hamiltonian, and starting point for the regularization, is required by functional differentiablity of the Hamiltonian constraint. The…

We study the (generalized) transition probability spaces, in the sense of Mielnik and Cantoni, for spacetime quantum states in loop quantum gravity. First, we show that loop quantum gravity admits the structures of transition probability…