Related papers: On the interpretation of relativistic spin network…
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…
The purpose of this note is to make several advances in the interpretation of the balanced state sum model by Barrett and Crane in gr-qc/9709028 as a quantum theory of gravity. First, we outline a shortcoming of the definition of the model…
Barrett and Crane have proposed a model of simplicial Euclidean quantum gravity in which a central role is played by a class of Spin(4) spin networks called "relativistic spin networks" which satisfy a series of physically motivated…
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…
The general solutin to the constraints that define relativistic spin networks vertices is given and their relations with 3-dimensional quantum tetrahedra is dicussed. An alternative way to handle the constraints is also presented.
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…
This is a review paper about one of the approaches to unify Quantum Mechanics and the theory of General Relativity. Starting from the pioneer work of Regge and Penrose other scientists have constructed state sum models, as Feymann path…
We propose a new type of state sum model for two-dimensional surfaces that takes into account topology and spin. The definition used - new to the literature - provides a rich class of extended models called spin models. Both examples and…
The evaluation of a relativistic spin network for the classical case of the Lie group SU(2) is given by an integral formula over copies of SU(2). For the graph determined by a 4-simplex this gives the evaluation as an integral over a space…
The status of our understanding of relativistic sum rules is reviewed. The recent development of new theoretical methods for the evaluation of these sum rules offers hope for further advances in this challenging field. These new techniques…
In this work we provide explicit calculations that support the conclusions stated in Phys. Rev. Lett. 111, 039102 (2013) (comment), regarding recent literature on transverse polarization. We also compare and contrast two methods of deriving…
We explain the connection between the generalized spin quantities we have recently introduced and standard forms. We show how the calculation of various quantities of interest using these new forms is done. Focusing attention on expectation…
We analyse the sensitivity of a spin chain modelled by an undirected weighted connected graph exhibiting perfect state transfer to small perturbations in readout time and edge weight in order to obtain physically relevant bounds on the…
In this work, we present a comprehensive treatment of weighted random sampling (WRS) over data streams. More precisely, we examine two natural interpretations of the item weights, describe an existing algorithm for each case ([2, 4]),…
We review the state approach to toss juggling and extend the approach to spin juggling, a new concept. We give connections to current research on random juggling and describe a professional-level juggling performance that further…
We give a short review of the spin foam models of quantum gravity, with an emphasis on the Barret-Crane model. After explaining the shortcomings of the Barret-Crane model, we briefly discuss two new approaches, one based on the 3d spin foam…
In part I of [1] we have developed the tensor and spin representation of SO(4) in order to apply it to the simplicial decomposition of the Barrett-Crane model. We attach to each face of a triangle the spherical function constructed from the…
The roles that spin networks play in gauge theories, quantum gravity and topological quantum field theory are briefly described, with an emphasis on the question of the relationships among them. It is argued that spin networks and their…
Entangled EPR spin pairs can be treated using the statistical ensemble interpretation of quantum mechanics. As such the singlet state results from an ensemble of spin pairs each with an arbitrary axis of quantization. This axis acts as 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…