Spin Networks in Nonperturbative Quantum Gravity

  title={Spin Networks in Nonperturbative Quantum Gravity},
  author={John C. Baez},
  journal={arXiv: General Relativity and Quantum Cosmology},
  • J. Baez
  • Published 21 April 1995
  • Physics
  • arXiv: General Relativity and Quantum Cosmology
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 topological quantum eld theory, functional integration on the spaceA=G of connections modulo gauge transformations, and the loop representation of quantum gravity. Here, after an introduction to the basic ideas of nonperturbative canonical quantum gravity, we… 
Spin networks and quantum gravity.
  • Rovelli, Smolin
  • Physics
    Physical review. D, Particles and fields
  • 1995
A new basis on the state space of non-perturbative quantum gravity is introduced that allows a simple expression for the exact solutions of the Hamiltonian constraint (Wheeler-DeWitt equation) that have been discovered in the loop representation.
Spin networks for noncompact groups
Spin networks are a natural generalization of Wilson loop 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
Integrability for relativistic 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
Existence of spinorial states in pure loop quantum gravity
We demonstrate the existence of spinorial states in a kinematical theory of canonical quantum gravity without matter. This should be regarded as evidence in support of the conjecture that bound
Learning about quantum gravity with a couple of nodes
Loop Quantum Gravity provides a natural truncation of the infinite degrees of freedom of gravity, obtained by studying the theory on a given finite graph. We review this procedure and we present the
Higher-Dimensional Algebra and Planck-Scale Physics
This is a nontechnical introduction to recent work on quantum gravity using ideas from higher-dimensional algebra. We argue that reconciling general relativity with the Standard Model requires a
Fate of the Hoop Conjecture in Quantum Gravity.
Using the concentration of measure phenomenon, it is proved that, whenever the ratio between the boundary ∂R and the bulk edges of the graph overcomes a finite threshold, the state of the boundary is always thermal, with an entropy proportional to its area.
Supersymmetric spin networks
In this article we study the construction of supersymmetric spin networks, which has a direct interpretation in context of the representation theory of the superalgebra. In particular we analyze a
Separable Hilbert space in loop quantum gravity
We study the separability of the state space of loop quantum gravity. In the standard construction, the kinematical Hilbert space of the diffeomorphism-invariant states is nonseparable. This is a
On Geometry and Symmetries in Classical and Quantum Theories of Gauge Gravity
Spin Foam and Loop approaches to Quantum Gravity reformulate Einstein's theory of relativity in terms of connection variables. The metric properties are encoded in face bivectors/conjugate fluxes


Spin network states in gauge theory
Abstract Given a real-analytic manifoldM, a compact connected Lie groupGand a principalG-bundleP→M, there is a, canonical “generalized measure” on the space A / G of smooth connections onPmodulo
Knots and quantum gravity: Progress and prospects
Recent work on the loop representation of quantum gravity has revealed previously unsuspected connections between knot theory and quantum gravity, or more generally, 3-dimensional topology and
Spin networks, Turaev-Viro theory and the loop representation
We investigate the Ponzano-Regge and Turaev-Viro topological quantum field theories using spin networks and their q-deformed analogues. We propose a new description of the state space for the
Topological quantum field theories from generalized 6j symbols
Given an associative algebra with a distinguished finite set of representations that is closed under a (deformed) tensor product, and satisfies some technical assumptions, we define generalized
Coherent State Transforms for Spaces of Connections
Abstract The Segal–Bargmann transform plays an important role in quantum theories of linear fields. Recently, Hall obtained a non-linear analog of this transform for quantum mechanics on Lie groups.
(2+1)-Dimensional Gravity as an Exactly Soluble System
Representations of the holonomy algebras of gravity and nonAbelian gauge theories
Holonomy algebras arise naturally in the classical description of Yang-Mills fields and gravity, and it has been suggested, at a heuristic level, that they may also play an important role in a