Related papers: Area Propagator and Boosted Spin Networks in Loop …

In this paper, I show that if a spin network is cut by a surface separating space-time into two regions, the sum of spins of edges crossing the surface must be an integer. This gives a restriction on the area spectrum of such surfaces,…

Quantum spin networks overcome the challenges of traditional charge-based electronics by encoding the information into spin degrees of freedom. Although beneficial for transmitting information with minimal losses when compared to their…

The spin network quantum simulator relies on the su(2) representation ring (or its q-deformed counterpart at q= root of unity) and its basic features naturally include (multipartite) entanglement and braiding. In particular, q-deformed spin…

The formula for the area eigenvalues that was obtained by many authors within the approach known as loop quantum gravity states that each edge of a spin network contributes an area proportional to sqrt{j(j+1)} times Planck length squared to…

Spin networks in Loop Quantum Gravity are traditionally described by unitary holonomies corresponding to noiseless transformations. In this work, we extend this framework to incorporate general quantum channels that model effects of…

We investigate the multipartite entanglement of a uniformly curved quantum 3D space region with boundary, realised in terms of spin networks defined on a graph with non trivial SU(2) holonomies, in the framework of loop quantum gravity. The…

The dual picture of quantum geometry provided by a spin network state is discussed. From this perspective, we introduce a new operator in Loop Quantum Gravity - the length operator. We describe its quantum geometrical meaning and derive…

In loop quantum gravity, the area element of embedded spatial surfaces is given by a well-defined operator. We further characterize the quantized geometry of such surfaces by proposing definitions for operators quantizing scalar curvature…

Spin networks are at the core of quantum gravity. Our aim is to plug the mathematical community at large into the procedures turn to create a finite quantum theory of general relativity. For this, because of the different cultural…

The state space of Loop Quantum Gravity admits a decomposition into orthogonal subspaces associated to diffeomorphism equivalence classes of spin-network graphs. In this paper I investigate the possibility of obtaining this state space from…

We propose a new notation for the states in some models of quantum gravity, namely 4-valent spin networks embedded in a topological three manifold. With the help of this notation, equivalence moves, namely translations and rotations, can be…

We construct in this article a new realization of quantum geometry, which is obtained by quantizing the recently-introduced flux formulation of loop quantum gravity. In this framework, the vacuum is peaked on flat connections, and states…

The mathematical apparatus of quantum--mechanical angular momentum (re)coupling, developed originally to describe spectroscopic phenomena in atomic, molecular, optical and nuclear physics, is embedded in modern algebraic settings which…

In the long-standing quest to reconcile gravity with quantum mechanics, profound connections have been unveiled between concepts traditionally pertaining to quantum information theory, such as entanglement, and constitutive features of…

The spin network simulator model represents a bridge between (generalized) circuit schemes for standard quantum computation and approaches based on notions from Topological Quantum Field Theories (TQFT). More precisely, when working with…

We describe how a spin-foam state sum model can be reformulated as a quantum field theory of spin networks, such that the Feynman diagrams of that field theory are the spin-foam amplitudes. In the case of open spin networks, we obtain a new…

Relativistic spin networks are defined by considering the spin covering of the group SO(4), SU(2) times SU(2). Relativistic quantum spins are related to the geometry of the 2-dimensional faces of a 4-simplex. This extends the idea of…

It is well known that the SU(2)-gauge invariant phase space of loop gravity can be represented in terms of twisted geometries. These are piecewise-linear-flat geometries obtained by gluing together polyhedra, but the resulting geometries…

The continuum limit of loop quantum gravity is still an open problem. Indeed, no proper dynamics in known to start with and we still lack the mathematical tools to study its would-be continuum limit. In the present PhD dissertation, we will…

We develop a new perspective on the discretization of the phase space structure of gravity in 2+1 dimensions as a piecewise-flat geometry in 2 spatial dimensions. Starting from a subdivision of the continuum geometric and phase space…