6 research outputs found
The complete LQG propagator: II. Asymptotic behavior of the vertex
In a previous article we have show that there are difficulties in obtaining
the correct graviton propagator from the loop-quantum-gravity dynamics defined
by the Barrett-Crane vertex amplitude. Here we show that a vertex amplitude
that depends nontrivially on the intertwiners can yield the correct propagator.
We give an explicit example of asymptotic behavior of a vertex amplitude that
gives the correct full graviton propagator in the large distance limit.Comment: 16 page
On the relation between the connection and the loop representation of quantum gravity
Using Penrose binor calculus for () tensor expressions, a
graphical method for the connection representation of Euclidean Quantum Gravity
(real connection) is constructed. It is explicitly shown that: {\it (i)} the
recently proposed scalar product in the loop-representation coincide with the
Ashtekar-Lewandoski cylindrical measure in the space of connections; {\it (ii)}
it is possible to establish a correspondence between the operators in the
connection representation and those in the loop representation. The
construction is based on embedded spin network, the Penrose graphical method of
calculus, and the existence of a generalized measure on the space of
connections modulo gauge transformations.Comment: 19 pages, ioplppt.sty and epsfig.st
Matrix Elements of Thiemann's Hamiltonian Constraint in Loop Quantum Gravity
We present an explicit computation of matrix elements of the hamiltonian
constraint operator in non-perturbative quantum gravity. In particular, we
consider the euclidean term of Thiemann's version of the constraint and compute
its action on trivalent states, for all its natural orderings. The calculation
is performed using graphical techniques from the recoupling theory of colored
knots and links. We exhibit the matrix elements of the hamiltonian constraint
operator in the spin network basis in compact algebraic form.Comment: 32 pages, 22 eps figures. LaTeX (Using epsfig.sty,ioplppt.sty and
bezier.sty). Submited to Classical and Quantum Gravit
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