Related papers: Three mathematical faces of SU(2) - spin networks
I suggest that the Spin-Statistics connection is a consequence of the phase shifts on quantum scattering amplitudes due to the induced gravitomagnetic field of the whole Universe at critical density. This connection was recently brought out…
We introduce a quantum volume operator $K$ in three--dimensional Quantum Gravity by taking into account a symmetrical coupling scheme of three SU(2) angular momenta. The spectrum of $K$ is discrete and defines a complete set of eigenvectors…
Mapping-class groups of 3-manifolds feature as symmetry groups in canonical quantum gravity. They are an obvious source through which topological information could be transmitted into the quantum theory. If treated as gauge symmetries,…
Spin bases of relevance for quantum systems with cyclic symmetry as well as for quantum information and quantum computation are constructed from the theory of angular momentum. This approach is connected to the use of generalized Pauli…
A hidden gauge theory structure of quantum mechanics which is invisible in its conventional formulation is uncovered. Quantum mechanics is shown to be equivalent to a certain Yang-Mills theory with an infinite-dimensional gauge group and a…
This is an introduction to quantum gravity, aimed at a fairly general audience and concentrating on what have historically two main approaches to quantum gravity: the covariant and canonical programs (string theory is not covered). The…
A particular approach to topology change in quantum gravity is reviewed, showing that several aspects of Stephen's work are intertwined with it in an essential way. Speculations are made on possible implications for the causal set approach…
This thesis is dedicated to the study of open spin networks. We formulate quasi-local descriptions of loop quantum gravity. We investigate the coarse-graining procedure via tracing over bulk degrees of freedom, which encodes all that we can…
We highlight the structure and properties of an abstract approach to quantum cosmology and gravity, dubbed $SU(\infty)$-QGR. Beginning from the concept of the Universe as an isolated quantum system, the main axiom of is the existence of an…
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 `background-free quantum theory with local…
The purpose of these lectures is to discuss in some detail a new, non-perturbative approach to quantum gravity. I would like to present the basic ideas, outline the key results that have been obtained so far and indicate where we are headed…
It is well known that the SU(2)-gauge invariant phase space of loop gravity can be represented in terms of twisted geometries. These are piecewise-linear-flat geometries obtained by gluing together polyhedra, but the resulting geometries…
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…
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…
The present thesis is divided into two main research areas: Classical Cosmology and (Loop) Quantum Gravity. The first part concerns cosmological models with one phantom and one scalar field, that provide the `super-accelerated' scenario not…
A new functional calculus, developed recently for a fully non-perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. Regulated operators corresponding to areas of 2-surfaces…
The quantum principle of relativity (QPR) puts forward an ambitious idea: extend special relativity with a formally superluminal branch of Lorentz-type maps, and treat the resulting consistency constraints as hints about why quantum theory…
The aim of this paper is to explain carefully the arguments behind the assertion that the correct quantum theory of gravity must be background independent. We begin by recounting how the debate over whether quantum gravity must be…
The quantum group structure of the Liouville theory is reviewd and shown to be an important tool for solving the theory.
We describe how a spin-foam state sum model can be reformulated as a quantum field theory of spin networks, such that the Feynman diagrams of that field theory are the spin-foam amplitudes. In the case of open spin networks, we obtain a new…