相关论文: Invariants of Spin Networks from Braided Ribbon Ne…

The setting of Braided Ribbon Networks is used to present a general result in spin-networks embedded in manifolds: the existence of an infinite number of species of conserved quantities. Restricted to three-valent networks the number of…

We present a consistent definition for braided ribbon networks in 3-dimensional manifolds, unifying both three and four valent networks in a single framework. We present evolution moves for these networks which are dual to the Pachner moves…

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…

We propose a new notation for the states in some models of quantum gravity, namely 4-valent spin networks embedded in a topological three manifold. With the help of this notation, equivalence moves, namely translations and rotations, can be…

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…

Virtual knot theory is a generalization of knot theory which is based on Gauss chord diagrams and link diagrams on closed oriented surfaces. A twisted knot is a generalization of a virtual knot, which corresponds to a link diagram on a…

We summarize recent developments at the interface of quantum gravity and quantum information, and discuss applications to the quantum geometry of space in loop quantum gravity. In particular, we describe the notions of link entanglement,…

We review and present a few new results of the program of emergent matter as braid excitations of quantum geometry that is represented by braided ribbon networks. These networks are a generalisation of the spin networks proposed by Penrose…

An overview of microlocality in braided ribbon networks is presented. Following this, a series of definitions are presented to explore the concept of microlocality and the topology of ribbon networks. Isolated substructure of ribbon…

We discuss the extension of loop quantum gravity to topspin networks, a proposal which allows topological information to be encoded in spin networks. We will show that this requires minimal changes to the phase space, C*-algebra and Hilbert…

Construction of representations of braid group generators from $N$-state vertex models provide an elegant route to study knot and link invariants. Using such a braid group representation, an algebraic formula for the link invariants was put…

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,…

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…

Non-perturbative approaches to quantum gravity call for a deep understanding of the emergence of geometry and locality from the quantum state of the gravitational field. Without background geometry, the notion of distance should entirely…

We study the invariants of spin networks embedded in a three-dimensional manifold which are based on the path integral for SU(2) BF-Theory. These invariants appear naturally in Loop Quantum Gravity, and have been defined as spin-foam state…

We present an elementary introduction to one of the most important today knot theory approaches, which gives rise to a representation for a class of knot polynomials in terms of quantum groups. Historically, the approach was at the same…

Recent work suggests that topological features of certain quantum gravity theories can be interpreted as particles, matching the known fermions and bosons of the first generation in the Standard Model. This is achieved by identifying…

In loop quantum gravity approach to Planck scale physics, quantum geometry is represented by superposition of the so-called spin network states. In the recent literature, a class of spin networks promising from the perspective of quantum…

The spin network quantum simulator relies on the su(2) representation ring (or its q-deformed counterpart at q= root of unity) and its basic features naturally include (multipartite) entanglement and braiding. In particular, q-deformed spin…

We propose a gauge model of quantum electrodynamics (QED) and its nonabelian generalization from which we derive knot invariants such as the Jones polynomial. Our approach is inspired by the work of Witten who derived knot invariants from…