Related papers: Spin Networks and Recoupling in Loop Quantum Gravi…

The majority of current understanding of the quantum correlations is in the field of non-relativistic quantum mechanics. To develop quantum information and computation tasks fully, one must inevitably take into account the relativistic…

A new method for nonperturbative investigations of quantum gravity is presented in which the simplicial path integral is approximated by the partition function of a spin system. This facilitates analytical and numerical computations…

The relation between Loop Quantum Gravity and Regge calculus has been pointed out many times in the literature. In particular the large spin asymptotics of the Barrett-Crane vertex amplitude is known to be related to the Regge action. In…

In canonical quantum gravity, the presence of spatial boundaries naturally leads to a boundary quantum states, representing quantum boundary conditions for the bulk fields. As a consequence, quantum states of the bulk geometry needs to be…

We give a formal treatment of the "Correlated Worldline" theory of quantum gravity. The generating functional is written as a product over multiple copies of the coupled matter and gravitational fields; paths for fields are correlated via…

While the use of spin networks has greatly improved our understanding of the kinematical aspects of quantum gravity, the dynamical aspects remain obscure. To address this problem, we define the concept of a `spin foam' going from one spin…

We connect Braided Ribbon Networks to the states of loop quantum gravity. Using this connection we present the reduced link as an invariant which captures information from the embedding of the spin-networks. We also present a means of…

The graphical calculus method is generalized to study the relation between covariant and canonical dynamics of loop quantum gravity. On one hand, a graphical derivation of the partition function of the generalized Euclidean…

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…

The evaluation of relativistic spin networks plays a fundamental role in the Barrett-Crane state sum model of Lorentzian quantum gravity in 4 dimensions. A relativistic spin network is a graph labelled by unitary irreducible representations…

Spin chains can be used to describe a wide range of platforms for quantum computation and quantum information. They enable the understanding, demonstration, and modeling of numerous useful phenomena, such as high fidelity transfer of…

We derive the Gauss-Codazzi equation in the holonomy and plane-angle representations and we use the result to write a Gauss-Codazzi equation for a discrete (2+1)-dimensional manifold, triangulated by isosceles tetrahedra. This allows us to…

We perform a quantization of the loop gravity phase space purely in terms of spinorial variables, which have recently been shown to provide a direct link between spin network states and simplicial geometries. The natural Hilbert space to…

We perform a rigorous piecewise-flat discretization of classical general relativity in the first-order formulation, in both 2+1 and 3+1 dimensions, carefully keeping track of curvature and torsion via holonomies. We show that the resulting…

This paper constructs a kinematic basis for spin networks with planar or cylindrical symmetry, by exploiting the fact that the basis elements are representations of an O(3) subgroup of O(4). The action of the volume operator on this basis…

This is the second paper in the series to introduce a graphical method to loop quantum gravity. We employ the graphical method as a powerful tool to calculate the actions of the Euclidean Hamiltonian constraint operator and the so-called…

In the emerging quantum internet, complex network topology could lead to efficient quantum communication and enhanced robustness against failures. However, there are some concerns about complexity in quantum communication networks, such as…

Remarkable efforts in the study of the semi-classical regime of kinematical loop quantum gravity are currently underway. In this note, we construct a ``quasi-coherent'' weave state using Gaussian factors. In a similar fashion to some other…

The main features of quantum computing are described in the framework of spin resonance methods. Stress is put on the fact that quantum computing is in itself nothing but a re-interpretation (fruitful indeed) of well-known concepts. The…

We derive a geometric representation of couplings between spin degrees of freedom and gauge fields within the worldline approach to quantum field theory. We combine the string-inspired methods of the worldline formalism with elements of the…