3 research outputs found
Non-commutative flux representation for loop quantum gravity
The Hilbert space of loop quantum gravity is usually described in terms of
cylindrical functionals of the gauge connection, the electric fluxes acting as
non-commuting derivation operators. It has long been believed that this
non-commutativity prevents a dual flux (or triad) representation of loop
quantum gravity to exist. We show here, instead, that such a representation can
be explicitly defined, by means of a non-commutative Fourier transform defined
on the loop gravity state space. In this dual representation, flux operators
act by *-multiplication and holonomy operators act by translation. We describe
the gauge invariant dual states and discuss their geometrical meaning. Finally,
we apply the construction to the simpler case of a U(1) gauge group and compare
the resulting flux representation with the triad representation used in loop
quantum cosmology.Comment: 12 pages, matches published versio
Background Independent Quantum Gravity: A Status Report
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 geometry. Our presentation is pedagogical. Thus, in addition to
providing a bird's eye view of the present status of the subject, the article
should also serve as a vehicle to enter the field and explore it in detail. To
aid non-experts, very little is assumed beyond elements of general relativity,
gauge theories and quantum field theory. While the article is essentially
self-contained, the emphasis is on communicating the underlying ideas and the
significance of results rather than on presenting systematic derivations and
detailed proofs. (These can be found in the listed references.) The subject can
be approached in different ways. We have chosen one which is deeply rooted in
well established physics and also has sufficient mathematical precision to
ensure that there are no hidden infinities. In order to keep the article to a
reasonable size, and to avoid overwhelming non-experts, we have had to leave
out several interesting topics, results and viewpoints; this is meant to be an
introduction to the subject rather than an exhaustive review of it.Comment: 125 pages, 5 figures (eps format), the final version published in CQ