Related papers: Three mathematical faces of SU(2) - spin networks
Quantum gravity has been so elusive because we have tried to approach it by two paths which can never meet: quantum mechanics and general relativity. These contradict each other not only in superdense regimes, but also in the vacuum. We…
A major unsolved problem in theoretical physics is to reconcile the classical theory of general relativity with quantum mechanics. These lectures will deal with an attempt to describe quantum gravity as a path integral over geometries known…
We perform a rigorous piecewise-flat discretization of classical general relativity in the first-order formulation, in both 2+1 and 3+1 dimensions, carefully keeping track of curvature and torsion via holonomies. We show that the resulting…
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 quest for a consistent theory which describes the quantum microstructure of spacetime seems to require some departure from the paradigms that have been followed in the construction of quantum theories for the other fundamental…
The general solutin to the constraints that define relativistic spin networks vertices is given and their relations with 3-dimensional quantum tetrahedra is dicussed. An alternative way to handle the constraints is also presented.
Till now, the foundation of quantum physics is still mysterious. To explore the mysteries in the foundation of quantum physics, people always take it for granted that quantum processes must be some types of fields/objects on a rigid space.…
This is a self-contained introduction to quantum Riemannian geometry based on quantum groups as frame groups, and its proposed role in quantum gravity. Much of the article is about the generalisation of classical Riemannian geometry that…
The main results for the two-dimensional quantum gravity, conjectured from the matrix model or integrable approach, are presented in the form to be compared with the world-sheet or Liouville approach. In spherical limit the integrable side…
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 describe the application of methods from the study of discrete dynanmical systems to the problem of the continuum limit of evolving spin networks. These have been found to describe the small scale structure of quantum general relativity…
These notes are a didactic overview of the non perturbative and background independent approach to a quantum theory of gravity known as loop quantum gravity. The definition of real connection variables for general relativity, used as a…
A new approach to quantum gravity is described which joins the loop representation formulation of the canonical theory to the causal set formulation of the path integral. The theory assigns quantum amplitudes to special classes of causal…
In the context of a canonical quantization of general relativity, one can deform the loop gravity phase space on a graph by replacing the T*SU(2) phase space attached to each edge by SL(2,C) seen as a phase space. This deformation is…
A "quantum-first" approach to gravity is described, where rather than quantizing general relativity, one seeks to formulate the physics of gravity within a quantum-mechanical framework with suitably general postulates. Important guides are…
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…
We focus on three distinct lines of recent developments: edge modes and boundary charges in gravitational physics, relational dynamics in classical and quantum gravity, and quantum reference frames. We argue that these research directions…
Motivated by the expectation that relativistic symmetries might acquire quantum features in Quantum Gravity, we take the first steps towards a theory of ''Doubly'' Quantum Mechanics, a modification of Quantum Mechanics in which the…
The goal of this article is to present an introduction to loop quantum gravity -a background independent, non-perturbative approach to the problem of unification of general relativity and quantum physics, based on a quantum theory of…
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,…