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A Model of Three-Dimensional Lattice Gravity

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abstract

A model is proposed which generates all oriented $3d$ simplicial complexes weighted with an invariant associated with a topological lattice gauge theory. When the gauge group is $SU_q(2)$, $q^n=1,$ it is the Turaev-Viro invariant and the model may be regarded as a non-perturbative definition of $3d$ simplicial quantum gravity. If one takes a finite abelian group $G$, the corresponding invariant gives the rank of the first cohomology group of a complex \nolinebreak $C$: $I_G(C) = rank(H^1(C,G))$, which means a topological expansion in the Betti number $b^1$. In general, it is a theory of the Dijkgraaf-Witten type, $i.e.$ determined completely by the fundamental group of a manifold.

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2024 1

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Hilbert space formalisms for group field theory

gr-qc · 2024-12-10 · accept · novelty 3.0

A structured review of the three main Hilbert space formalisms for group field theory, with emphasis on their assumptions and conceptual connections.

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  • Hilbert space formalisms for group field theory gr-qc · 2024-12-10 · accept · none · ref 18 · internal anchor

    A structured review of the three main Hilbert space formalisms for group field theory, with emphasis on their assumptions and conceptual connections.