172 research outputs found
3-dimensional Gravity from the Turaev-Viro Invariant
We study the -deformed su(2) spin network as a 3-dimensional quantum
gravity model. We show that in the semiclassical continuum limit the
Turaev-Viro invariant obtained recently defines naturally regularized
path-integral la Ponzano-Regge, In which a contribution from
the cosmological term is effectively included. The regularization dependent
cosmological constant is found to be , where
. We also discuss the relation to the Euclidean Chern-Simons-Witten
gravity in 3-dimension.Comment: 11page
Surface embedding, topology and dualization for spin networks
Spin networks are graphs derived from 3nj symbols of angular momentum. The
surface embedding, the topology and dualization of these networks are
considered. Embeddings into compact surfaces include the orientable sphere S^2
and the torus T, and the not orientable projective space P^2 and Klein's bottle
K. Two families of 3nj graphs admit embeddings of minimal genus into S^2 and
P^2. Their dual 2-skeletons are shown to be triangulations of these surfaces.Comment: LaTeX 17 pages, 6 eps figures (late submission to arxiv.org
Semiclassical short strings in AdS_5 x S^5
We present results for the one-loop correction to the energy of a class of
string solutions in AdS_5 x S^5 in the short string limit. The computation is
based on the observation that, as for rigid spinning string elliptic solutions,
the fluctuation operators can be put into the single-gap Lame' form. Our
computation reveals a remarkable universality of the form of the energy of
short semiclassical strings. This may help to understand better the structure
of the strong coupling expansion of the anomalous dimensions of dual gauge
theory operators.Comment: 12 pages, one pdf figure. Invited Talk at 'Nonlinear Physics. Theory
and Experiment VI', Gallipoli (Italy) - June 23 - July 3, 201
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Autonomous biomorphic robots as platforms for sensors
The idea of building autonomous robots that can carry out complex and nonrepetitive tasks is an old one, so far unrealized in any meaningful hardware. Tilden has shown recently that there are simple, processor-free solutions to building autonomous mobile machines that continuously adapt to unknown and hostile environments, are designed primarily to survive, and are extremely resistant to damage. These devices use smart mechanics and simple (low component count) electronic neuron control structures having the functionality of biological organisms from simple invertebrates to sophisticated members of the insect and crab family. These devices are paradigms for the development of autonomous machines that can carry out directed goals. The machine then becomes a robust survivalist platform that can carry sensors or instruments. These autonomous roving machines, now in an early stage of development (several proof-of-concept prototype walkers have been built), can be developed so that they are inexpensive, robust, and versatile carriers for a variety of instrument packages. Applications are immediate and many, in areas as diverse as prosthetics, medicine, space, construction, nanoscience, defense, remote sensing, environmental cleanup, and biotechnology
Quantum mechanics of lattice gas automata. I. One particle plane waves and potentials
Classical lattice gas automata effectively simulate physical processes such
as diffusion and fluid flow (in certain parameter regimes) despite their
simplicity at the microscale. Motivated by current interest in quantum
computation we recently defined quantum lattice gas automata; in this paper we
initiate a project to analyze which physical processes these models can
effectively simulate. Studying the single particle sector of a one dimensional
quantum lattice gas we find discrete analogues of plane waves and wave packets,
and then investigate their behaviour in the presence of inhomogeneous
potentials.Comment: 19 pages, plain TeX, 14 PostScript figures included with epsf.tex
(ignore the under/overfull \vbox error messages), two additional large
figures available upon reques
Statistical mechanics of voting
Decision procedures aggregating the preferences of multiple agents can
produce cycles and hence outcomes which have been described heuristically as
`chaotic'. We make this description precise by constructing an explicit
dynamical system from the agents' preferences and a voting rule. The dynamics
form a one dimensional statistical mechanics model; this suggests the use of
the topological entropy to quantify the complexity of the system. We formulate
natural political/social questions about the expected complexity of a voting
rule and degree of cohesion/diversity among agents in terms of random matrix
models---ensembles of statistical mechanics models---and compute quantitative
answers in some representative cases.Comment: 9 pages, plain TeX, 2 PostScript figures included with epsf.tex
(ignore the under/overfull \vbox error messages
Discrete structures in gravity
Discrete approaches to gravity, both classical and quantum, are reviewed
briefly, with emphasis on the method using piecewise-linear spaces. Models of
3-dimensional quantum gravity involving 6j-symbols are then described, and
progress in generalising these models to four dimensions is discussed, as is
the relationship of these models in both three and four dimensions to
topological theories. Finally, the repercussions of the generalisations are
explored for the original formulation of discrete gravity using edge-length
variables.Comment: 30 pages, 4 figure
A class of elementary particle models without any adjustable real parameters
Conventional particle theories such as the Standard Model have a number of
freely adjustable coupling constants and mass parameters, depending on the
symmetry algebra of the local gauge group and the representations chosen for
the spinor and scalar fields. There seems to be no physical principle to
determine these parameters as long as they stay within certain domains dictated
by the renormalization group. Here however, reasons are given to demand that,
when gravity is coupled to the system, local conformal invariance should be a
spontaneously broken exact symmetry. The argument has to do with the
requirement that black holes obey a complementarity principle relating ingoing
observers to outside observers, or equivalently, initial states to final
states. This condition fixes all parameters, including masses and the
cosmological constant. We suspect that only examples can be found where these
are all of order one in Planck units, but the values depend on the algebra
chosen. This paper combines findings reported in two previous preprints, and
puts these in a clearer perspective by shifting the emphasis towards the
implications for particle models.Comment: 28 pages (incl. title page), no figure
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