Related papers: Holonomy operator for spin connection and spatial …
The evolution of spin network states in loop quantum gravity can be described by introducing a time variable, defined by the surfaces of constant value of an auxiliary scalar field. We regulate the Hamiltonian, generating such an evolution,…
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…
Gravity is uniquely situated in between classical topological field theories and standard local field theories. This can be seen in the the quasi-local nature of gravitational observables, but is nowhere more apparent than in gravity's…
The Koslowski-Sahlmann (KS) representation is a generalization of the representation underlying the discrete spatial geometry of Loop Quantum Gravity (LQG), to accommodate states labelled by smooth spatial geometries. As shown recently, the…
Considering as usual that the underlying geometry of our universe is well described by the spatially flat Friedmann-Lemaitre-Robertson-Walker line element, we review how the background of holonomy corrected Loop Quantum Cosmology (LQC)…
We give a prescription to define in Loop Quantum Gravity the electric field operator related to the scale factor of an homogeneous and isotropic cosmological space-time. This procedure allows to link the fundamental theory with its…
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.…
The volume operator plays a pivotal role for the quantum dynamics of Loop Quantum Gravity (LQG), both in the full theory and in truncated models adapted to cosmological situations coined Loop Quantum Cosmology (LQC). It is therefore crucial…
We propose that finite cutoff regions of holographic spacetimes represent quantum circuits that map between boundary states at different times and Wilsonian cutoffs, and that the complexity of those quantum circuits is given by the…
In this second paper on loop quantization of Gowdy model, we introduce the kinematical Hilbert space on which appropriate holonomies and fluxes are well represented. The quantization of the volume operator and the Gauss constraint is…
In a previous paper we showed that the phase space of loop quantum gravity on a fixed graph can be parametrized in terms of twisted geometries, quantities describing the intrinsic and extrinsic discrete geometry of a cellular decomposition…
We study holonomy algebras generated by an algebraic element of the Clifford algebra, or equivalently, the holonomy algebras of certain spin connections in flat space. We provide series of examples in arbitrary dimensions and establish…
The Hamiltonian formulation of scalar-tensor theories of gravity is derived from their Lagrangian formulation by Hamiltonian analysis. The Hamiltonian formalism marks off two sectors of the theories by the coupling parameter $\omega(\phi)$.…
Starting from a recently-introduced algebraic structure on spin foam models, we define a Hopf algebra by dividing with an appropriate quotient. The structure, thus defined, naturally allows for a mirror analysis of spin foam models with…
We introduce the Quantum Holonomy-Diffeomorphism *-algebra, which is generated by holonomy-diffeomorphisms on a 3-dimensional manifold and translations on a space of SU(2)-connections. We show that this algebra encodes the canonical…
The scalar-tensor theories of gravity in spacetime dimensions $D+1>2$ are studied. By doing Hamiltonian analysis, we obtain the geometrical dynamics of the theories from their Lagrangian. The Hamiltonian formalism indicates that the…
We give an alternative presentation of Khovanov homology of links with strict functoriality result over integers. The construction uses an oriented $sl(2)$ state model allowing a natural definition of the boundary operator as twisted action…
The Hamiltonian constraint remains an elusive object in loop quantum gravity because its action on spinnetworks leads to changes in their corresponding graphs. As a result, calculations in loop quantum gravity are often considered…
Loop quantum gravity methods are applied to a symmetry-reduced model with homogeneity in two dimensions, derived from a Gowdy model [5,6]. The conditions for propagation of unidirectional plane gravitational waves at exactly the speed of…
We summarize the basics of the loop representation of quantum gravity and describe the main aspects of the formalism, including its latest developments, in a reorganized and consistent form. Recoupling theory, in its graphical…