相关论文: Loop Representations

Inhomogeneous cosmological perturbation equations are derived in loop quantum gravity, taking into account corrections in particular in gravitational parts. This provides a framework for calculating the evolution of modes in structure…

We perform a quantization of the loop gravity phase space purely in terms of spinorial variables, which have recently been shown to provide a direct link between spin network states and simplicial geometries. The natural Hilbert space to…

The "loop equations" of random matrix theory are a hierarchy of equations born of attempts to obtain explicit formulae for generating functions of map enumeration problems. These equations, originating in the physics of 2-dimensional…

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,…

We introduce loop spaces (in the sense of derived algebraic geometry) into the representation theory of reductive groups. In particular, we apply the theory developed in our previous paper arXiv:1002.3636 to flag varieties, and obtain new…

In the loop representation the quantum constraints of gravity can be solved. This fact allowed significant progress in the understanding of the space of states of the theory. The analysis of the constraints over loop dependent wavefunctions…

In the past, the possibility to employ (scalar) material reference systems in order to describe classical and quantum gravity directly in terms of gauge invariant (Dirac) observables has been emphasised frequently. This idea has been picked…

The approaches to quantum field theories based in the so called loop representation deserved much attention recently. In it, closed curves and holonomies around them play a central role. In this framework the group of loops and the group of…

Abelian Gauge Theories are quantized in a geometric representation that generalizes the Loop Representation and treates electric and magnetic operators on the same footing. The usual canonical algebra is turned into a topological algebra of…

We apply a recent argument of Verlinde to loop quantum gravity, to conclude that Newton's law of gravity emerges in an appropriate limit and setting. This is possible because the relationship between area and entropy is realized in loop…

Cosmology appears as the most promising way to test and constrain quantum gravity theories. Loop quantum gravity is among the most advanced attempts to perform a non-perturbative quantization of general relativity. Its cosmological…

The standard picture of the loop expansion associates a factor of h-bar with each loop, suggesting that the tree diagrams are to be associated with classical physics, while loop effects are quantum mechanical in nature. We discuss examples…

Covariant models of loop quantum gravity generically imply dynamical signature change at high density. This article presents detailed derivations that show the fruitful interplay of this new kind of signature change with wave-function…

An assessment is offered of the progress that the major approaches to quantum gravity have made towards the goal of constructing a complete and satisfactory theory. The emphasis is on loop quantum gravity and string theory, although other…

Spherically symmetric models of loop quantum gravity have been studied recently by different methods that aim to deal with structure functions in the usual constraint algebra of gravitational systems. As noticed by Gambini and Pullin, a…

Starting from a generic generally covariant classical theory we introduce the logarithmic correction to the quantum wave equation. We demonstrate the emergence of the evolution time from the group of automorphisms of the von Neumann algebra…

The linear canonical transforms of position and momentum are used to construct the tomographic probability representation of quantum states where the fair probability distribution determines the quantum state instead of the wave function or…

Some time ago it was conjectured that the coefficients of an expansion of the Jones polynomial in terms of the cosmological constant could provide an infinite string of knot invariants that are solutions of the vacuum Hamiltonian constraint…

We review aspects of loop quantum gravity and spin foam models at an introductory level, with special attention to questions frequently asked by non-specialists.

This paper explores the idea that within the framework of three-dimensional quantum gravity one can extend the notion of Feynman diagram to include the coupling of the particles in the diagram with quantum gravity. The paper concentrates on…