9,080 research outputs found
Loop Quantum Gravity
The problem of finding the quantum theory of the gravitational field, and
thus understanding what is quantum spacetime, is still open. One of the most
active of the current approaches is loop quantum gravity. Loop quantum gravity
is a mathematically well-defined, non-perturbative and background independent
quantization of general relativity, with its conventional matter couplings. The
research in loop quantum gravity forms today a vast area, ranging from
mathematical foundations to physical applications. Among the most significative
results obtained are: (i) The computation of the physical spectra of
geometrical quantities such as area and volume; which yields quantitative
predictions on Planck-scale physics. (ii) A derivation of the
Bekenstein-Hawking black hole entropy formula. (iii) An intriguing physical
picture of the microstructure of quantum physical space, characterized by a
polymer-like Planck scale discreteness. This discreteness emerges naturally
from the quantum theory and provides a mathematically well-defined realization
of Wheeler's intuition of a spacetime ``foam''. Long standing open problems
within the approach (lack of a scalar product, overcompleteness of the loop
basis, implementation of reality conditions) have been fully solved. The weak
part of the approach is the treatment of the dynamics: at present there exist
several proposals, which are intensely debated. Here, I provide a general
overview of ideas, techniques, results and open problems of this candidate
theory of quantum gravity, and a guide to the relevant literature.Comment: Review paper written for the electronic journal `Living Reviews'. 34
page
Oriented matroid theory and loop quantum gravity in (2+2) and eight dimensions
We establish a connection between oriented matroid theory and loop quantum
gravity in (2+2) (two time and two space dimensions) and 8-dimensions. We start
by observing that supersymmetry implies that the structure constants of the
real numbers, complex numbers, quaternions and octonions can be identified with
the chirotope concept. This means, among other things, that normed divisions
algebras, which are only possible in 1,2, 4 or 8-dimensions, are linked to
oriented matroid theory. Therefore, we argue that the possibility for
developing loop quantum gravity in 8-dimensions must be taken as important
alternative. Moreover, we show that in 4-dimensions, loop quantum gravity
theories in the (1+3) or (0+4) signatures are not the only possibilities. In
fact, we show that loop quantum gravity associated with the (2+2)-signature may
also be an interesting physical structure.Comment: 13 pages, Late
Extended Loop Quantum Gravity
We discuss constraint structure of extended theories of gravitation (also
known as f(R) theories) in the vacuum selfdual formulation introduced in ref.
[1].Comment: 7 pages, few typos correcte
Relativistic Planck-scale polymer
Polymer quantum mechanics has been studied as a simplified picture that
reflects some of the key properties of Loop Quantum Gravity; however, while the
fate of relativistic symmetries in Loop Quantum Gravity is still not
established, it is usually assumed that the discrete polymer structure should
lead to a breakdown of relativistic symmetries. We here focus for simplicity on
a one-spatial-dimension polymer model and show that relativistic symmetries are
deformed, rather than being broken. The specific type of deformed relativistic
symmetries which we uncover appears to be closely related to analogous
descriptions of relativistic symmetries in some noncommutative spacetimes. This
also contributes to an ongoing effort attempting to establish whether the
"quantum-Minkowski limit" of Loop Quantum Gravity is a noncommutative
spacetime.Comment: 5 pages, no figures. v2: minor changes in Section I
Introduction to Loop Quantum Gravity
This article is based on the opening lecture at the third quantum geometry
and quantum gravity school sponsored by the European Science Foundation and
held at Zakopane, Poland in March 2011. The goal of the lecture was to present
a broad perspective on loop quantum gravity for young researchers. The first
part is addressed to beginning students and the second to young researchers who
are already working in quantum gravity.Comment: 30 pages, 2 figures. arXiv admin note: substantial text overlap with
arXiv:gr-qc/041005
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