Related papers: Supersymmetric Spin Networks and Quantum Supergrav…
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…
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…
The dual picture of quantum geometry provided by a spin network state is discussed. From this perspective, we introduce a new operator in Loop Quantum Gravity - the length operator. We describe its quantum geometrical meaning and derive…
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…
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,…
Utilizing the previously established general formalism for quantum symmetry reduction in the framework of loop quantum gravity the spectrum of the area operator acting on spherically symmetric states in 4 dimensional pure gravity is…
Loop Quantum Gravity defines the quantum states of space geometry as spin networks and describes their evolution in time. We reformulate spin networks in terms of harmonic oscillators and show how the holographic degrees of freedom of the…
Inspired by the spin geometry theorem, two operators are defined which measure angles in the quantum theory of geometry. One operator assigns a discrete angle to every pair of surfaces passing through a single vertex of a spin network. This…
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 discrete picture of geometry arising from the loop representation of quantum gravity can be extended by a quantum deformation. The operators for area and volume defined in the q-deformation of the theory are partly diagonalized. The…
We consider a supersymmetric extension of quantum gauge theory based on a vector multiplet containing supersymmetric partners of spin 3/2 for the vector fields. The constructions of the model follows closely the usual construction of gauge…
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.…
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…
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…
Quantum states of geometry in loop quantum gravity are defined as spin networks, which are graph dressed with SU(2) representations. A spin network edge carries a half-integer spin, representing basic quanta of area, and the standard…
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…
General non-commutative supersymmetric quantum mechanics models in two and three dimensions are constructed and some two and three dimensional examples are explicitly studied. The structure of the theory studied suggest other possible…
A spin network is a cubic ribbon graph labeled by representations of $\mathrm{SU}(2)$. Spin networks are important in various areas of Mathematics (3-dimensional Quantum Topology), Physics (Angular Momentum, Classical and Quantum Gravity)…
In this paper we investigate the finite-size properties of the spectrum of quantum spin chains with local spins taken to be the fundamental vector representation of the $OSp(n|2m)$ superalgebra.
We introduce a new basis on the state space of non-perturbative quantum gravity. The states of this basis are linearly independent, are well defined in both the loop representation and the connection representation, and are labeled by a…