Related papers: Asymptotics of classical spin networks
A classical spin network consists of a ribbon graph (i.e., an abstract graph with a cyclic ordering of the vertices around each edge) and an admissible coloring of its edges by natural numbers. The standard evaluation of a spin network is…
A spin network is a generalization of a knot or link: a graph embedded in space, with edges labelled by representations of a Lie group, and vertices labelled by intertwining operators. Such objects play an important role in 3-dimensional…
Spin networks, essentially labeled graphs, are ``good quantum numbers'' for the quantum theory of geometry. These structures encompass a diverse range of techniques which may be used in the quantum mechanics of finite dimensional systems,…
We study classical spin networks with group SU(2). In the first part, using gaussian integrals, we compute their generating series in the case where the networks are equipped with holonomies; this generalizes Westbury's formula. In the…
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…
Increasing interest is being dedicated in the last few years to the issues of exact computations and asymptotics of spin networks. The large-entries regimes (semiclassical limits) occur in many areas of physics and chemistry, and in…
Spin networks, the quantum states of discrete geometry in loop quantum gravity, are directed graphs whose links are labeled by irreducible representations of SU(2), or spins. Cosmic strings are 1-dimensional topological defects carrying…
We analyze the large-spin asymptotics of a class of spin-network wavefunctions of Euclidean Loop Quantum Gravity, which corresponds to a flat spacetime. A wavefunction from this class can be represented as a sum over the spins of an…
This article presents and discusses in detail the results of extensive exact calculations of the most basic ingredients of spin networks, the Racah coefficients (or Wigner 6j symbols), exhibiting their salient features when considered as a…
Given a real-analytic manifold M, a compact connected Lie group G and a principal G-bundle P -> M, there is a canonical `generalized measure' on the space A/G of smooth connections on P modulo gauge transformations. This allows one to…
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 expand a set of notions recently introduced providing the general setting for a universal representation of the quantum structure on which quantum information stands. The dynamical evolution process associated with generic quantum…
Let G be a compact Lie group. Using suitable normalization conventions, we show that the evaluation of GxG-symmetric spin networks is non-negative whenever the edges are labeled by representations of the form V\otimes V^* where V is a…
A method to evaluate spin networks for (2+1)-dimensional quantum gravity is given. We analyse the evaluation of spin networks for Lorentzian, Euclidean and a new limiting case of Newtonian quantum gravity. Particular attention is paid to…
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…
We define supersymmetric spin networks, which provide a complete set of gauge invariant states for supergravity and supersymmetric gauge theories. The particular case of Osp(1/2) is studied in detail and applied to the non-perturbative…
The stationary phase technique is used to calculate asymptotic formulae for SO(4) Relativistic Spin Networks. For the tetrahedral spin network this gives the square of the Ponzano-Regge asymptotic formula for the SU(2) 6j symbol. For the…
Spin networks are natural generalization of Wilson loops functionals. They have been extensively studied in the case where the gauge group is compact and it has been shown that they naturally form a basis of gauge invariant observables.…
In this paper we give a general introduction to supersymmetric spin networks. Its construction has a direct interpretation in context of the representation theory of the superalgebra. In particular we analyze a special kind of spin networks…
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…