3,959 research outputs found
The asymptotics of an amplitude for the 4-simplex
An expression for the oscillatory part of an asymptotic formula for the
relativistic spin network amplitude for a 4-simplex is given. The amplitude
depends on specified areas for each two-dimensional face in the 4-simplex. The
asymptotic formula has a contribution from each flat Euclidean metric on the
4-simplex which agrees with the given areas. The oscillatory part of each
contribution is determined by the Regge calculus Einstein action for that
geometry.Comment: 5 pages amstex, typos correcte
Relaxed Game Chromatic Numbers of Complete Multipartite Graphs
Competitive graph coloring is investigated by studying a game with two players, Alice and Bob, on a finite graph G with a set of r colors. Alice and Bob alternately color the vertices of G with legal colors. In the k-relaxed coloring game, a color c is legal for a vertex v if v has at most k neighbors previously colored c. New results about the 0, 1, and 2-relaxed game chromatic numbers will be presented, completely classifying the 0 and 1-relaxed games and partially classifying the 2-relaxed game. These results will be presented in the context of previous research and given a direction of where they need to go next
Tullio Regge's legacy: Regge calculus and discrete gravity
The review paper "Discrete Structures in Physics", written in 2000, describes
how Regge's discretization of Einstein's theory has been applied in classical
relativity and quantum gravity. Here, developments since 2000 are reviewed
briefly, with particular emphasis on progress in quantum gravity through spin
foam models and group field theories.Comment: 15 pages; a contribution to the forthcoming volume "Tullio Regge: an
eclectic genius, from quantum gravity to computer play", Eds. L Castellani,
A. Ceresole, R. D'Auria and P. Fr\`e (World Scientific); v2: added references
to more relevant work, minor changes to the tex
A note on area variables in Regge calculus
We consider the possibility of setting up a new version of Regge calculus in
four dimensions with areas of triangles as the basic variables rather than the
edge-lengths. The difficulties and restrictions of this approach are discussed.Comment: 4 pages, amstex. Revision has minor changes and more precise
conclusion
Feynman diagams coupled to three-dimensional quantum gravity
A framework for quantum field theory coupled to three-dimensional quantum
gravity is proposed. The coupling with quantum gravity regulates the Feynman
diagrams. One recovers the usual Feynman amplitudes in the limit as the
cosmological constant tends to zero.Comment: 7 pages. v2: minor corrections, added re
Asymptotics of Relativistic Spin Networks
The stationary phase technique is used to calculate asymptotic formulae for
SO(4) Relativistic Spin Networks. For the tetrahedral spin network this gives
the square of the Ponzano-Regge asymptotic formula for the SU(2) 6j symbol. For
the 4-simplex (10j-symbol) the asymptotic formula is compared with numerical
calculations of the Spin Network evaluation. Finally we discuss the asymptotics
of the SO(3,1) 10j-symbol.Comment: 31 pages, latex. v3: minor clarification
The asymptotics of an amplitude for the 4-simplex
An expression for the oscillatory part of an asymptotic formula for the relativistic spin network amplitude for a 4-simplex is given. The amplitude depends on specified areas for each two-dimensional face in the 4-simplex. The asymptotic formula has a contribution from each flat Euclidean metric on the 4-simplex which agrees with the given areas. The oscillatory part of each contribution is determined by the Regge calculus Einstein action for that geometry
Holonomy observables in Ponzano-Regge type state sum models
We study observables on group elements in the Ponzano-Regge model. We show
that these observables have a natural interpretation in terms of Feynman
diagrams on a sphere and contrast them to the well studied observables on the
spin labels. We elucidate this interpretation by showing how they arise from
the no-gravity limit of the Turaev-Viro model and Chern-Simons theory.Comment: 15 pages, 2 figure
A convergent and constraint-preserving finite element method for the p-harmonic flow into spheres
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