65,872 research outputs found
Invariants of 2+1 Quantum Gravity
In [1,2] we established and discussed the algebra of observables for 2+1
gravity at both the classical and quantum level. Here our treatment broadens
and extends previous results to any genus with a systematic discussion of
the centre of the algebra. The reduction of the number of independent
observables to is treated in detail with a precise
classification for and .Comment: 10 pages, plain TEX, no figures, DFTT 46/9
Chameleon Vector Bosons
We show that for a force mediated by a vector particle coupled to a conserved
U(1) charge, the apparent range and strength can depend on the size and density
of the source, and the proximity to other sources. This "chameleon" effect is
due to screening from a light charged scalar. Such screening can weaken
astrophysical constraints on new gauge bosons. As an example we consider the
constraints on chameleonic gauged B-L. We show that although Casimir
measurements greatly constrain any B-L force much stronger than gravity with
range longer than 0.1 microns, there remains an experimental window for a long
range chameleonic B-L force. Such a force could be much stronger than gravity,
and long or infinite range in vacuum, but have an effective range near the
surface of the earth which is less than a micron.Comment: 10 page
The Quantum Modular Group in (2+1)-Dimensional Gravity
The role of the modular group in the holonomy representation of
(2+1)-dimensional quantum gravity is studied. This representation can be viewed
as a "Heisenberg picture", and for simple topologies, the transformation to the
ADM "Schr{\"o}dinger picture" may be found. For spacetimes with the spatial
topology of a torus, this transformation and an explicit operator
representation of the mapping class group are constructed. It is shown that the
quantum modular group splits the holonomy representation Hilbert space into
physically equivalent orthogonal ``fundamental regions'' that are interchanged
by modular transformations.Comment: 23 pages, LaTeX, no figures; minor changes and clarifications in
response to referee (basic argument and conclusions unaffected
Quantum Holonomies in (2+1)-Dimensional Gravity
We describe an approach to the quantization of (2+1)--dimensional gravity
with topology R x T^2 and negative cosmological constant, which uses two
quantum holonomy matrices satisfying a q--commutation relation. Solutions of
diagonal and upper--triangular form are constructed, which in the latter case
exhibit additional, non--trivial internal relations for each holonomy matrix.
This leads to the notion of quantum matrix pairs. These are pairs of matrices
with non-commuting entries, which have the same pattern of internal relations,
q-commute with each other under matrix multiplication, and are such that
products of powers of the matrices obey the same pattern of internal relations
as the original pair. This has implications for the classical moduli space,
described by ordered pairs of commuting SL(2,R) matrices modulo simultaneous
conjugation by SL(2,R) matrices.Comment: 5 pages, to appear in the proceedings of 10th Marcel Grossmann
Meeting on Recent Developments in Theoretical and Experimental General
Relativity, Gravitation and Relativistic Field Theories (MG X MMIII), Rio de
Janeiro, Brazil, 20-26 Jul 200
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