58 research outputs found
Wave propagation on a random lattice
Motivated by phenomenological questions in quantum gravity, we consider the
propagation of a scalar field on a random lattice. We describe a procedure to
calculate the dispersion relation for the field by taking a limit of a periodic
lattice. We use this to calculate the lowest order coefficients of the
dispersion relation for a specific one-dimensional model.Comment: 13 pages, 3 figures. v3: Some minor changes and clarifications.
Virtually identical with the version published in Physical Review
Toward explaining black hole entropy quantization in loop quantum gravity
In a remarkable numerical analysis of the spectrum of states for a
spherically symmetric black hole in loop quantum gravity, Corichi, Diaz-Polo
and Fernandez-Borja found that the entropy of the black hole horizon increases
in what resembles discrete steps as a function of area. In the present article
we reformulate the combinatorial problem of counting horizon states in terms of
paths through a certain space. This formulation sheds some light on the origins
of this step-like behavior of the entropy. In particular, using a few extra
assumptions we arrive at a formula that reproduces the observed step-length to
a few tenths of a percent accuracy. However, in our reformulation the
periodicity ultimately arises as a property of some complicated process, the
properties of which, in turn, depend on the properties of the area spectrum in
loop quantum gravity in a rather opaque way. Thus, in some sense, a deep
explanation of the observed periodicity is still lacking.Comment: 15 pages, 5 figures. v3: final version (essentially as it appeared in
PRD
On the superselection theory of the Weyl algebra for diffeomorphism invariant quantum gauge theories
Much of the work in loop quantum gravity and quantum geometry rests on a
mathematically rigorous integration theory on spaces of distributional
connections. Most notably, a diffeomorphism invariant representation of the
algebra of basic observables of the theory, the Ashtekar-Lewandowski
representation, has been constructed. This representation is singled out by its
mathematical elegance, and up to now, no other diffeomorphism invariant
representation has been constructed. This raises the question whether it is
unique in a precise sense.
In the present article we take steps towards answering this question. Our
main result is that upon imposing relatively mild additional assumptions, the
AL-representation is indeed unique.
As an important tool which is also interesting in its own right, we introduce
a C*-algebra which is very similar to the Weyl algebra used in the canonical
quantization of free quantum field theories.Comment: 31 pages, no figures. v2: Instructive second method of proof
supplemente
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