5 research outputs found
2-Form Gravity of the Lorentzian Signature
We introduce a new spinorial, BF-like action for the Einstein gravity. This
is a first, up to our knowledge, 2-form action which describes the real,
Lorentzian gravity and uses only the self-dual connection. In the generic case,
the corresponding classical canonical theory is equivalent to the
Einstein-Ashtekar theory plus the reality conditions
On the structure of the space of generalized connections
We give a modern account of the construction and structure of the space of
generalized connections, an extension of the space of connections that plays a
central role in loop quantum gravity.Comment: 30 pages, added references, minor changes. To appear in International
Journal of Geometric Methods in Modern Physic
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
Diffeomorphism covariant representations of the holonomy-flux star-algebra
Recently, Sahlmann proposed a new, algebraic point of view on the loop
quantization. He brought up the issue of a star-algebra underlying that
framework, studied the algebra consisting of the fluxes and holonomies and
characterized its representations. We define the diffeomorphism covariance of a
representation of the Sahlmann algebra and study the diffeomorphism covariant
representations. We prove they are all given by Sahlmann's decomposition into
the cyclic representations of the sub-algebra of the holonomies by using a
single state only. The state corresponds to the natural measure defined on the
space of the generalized connections. This result is a generalization of
Sahlmann's result concerning the U(1) case.Comment: 37 pages, no figures, LaTeX2e, to be published in Class. Quant. Grav;
typos corrected, minor clarifying remark