19,735 research outputs found
The equality of 3-manifold invariants
The invariants of 3-manifolds defined by Kuperberg for involutory Hopf
algebras and those defined by the authors for spherical Hopf algebras are the
same for Hopf algebras on which they are both defined.Comment: 8 pages, definition of state sum invariant improved for clarity, plus
minor typos corrected. With 3 postscript figures. further change: BoxedEPSF
macro now include
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
Quantum Gravity as Topological Quantum Field Theory
The physics of quantum gravity is discussed within the framework of
topological quantum field theory. Some of the principles are illustrated with
examples taken from theories in which space-time is three dimensional.Comment: 23 pages, amstex, JMP special issue (deadline permitting). (Text not
changed
State sum models for quantum gravity
This paper reviews the construction of quantum field theory on a
4-dimensional spacetime by combinatorial methods, and discusses the recent
developments in the direction of a combinatorial construction of quantum
gravity.Comment: amslatex, 7 pages, ICMP conference tal
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