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Structure of Topological Lattice Field Theories in Three Dimensions | | Stephen-wei Chung
; Masafumi Fukuma
; Alfred Shapere
; | | Date: |
19 May 1993 | | Journal: | Int.J.Mod.Phys. A9 (1994) 1305-1360 | | Subject: | High Energy Physics - Theory; Quantum Algebra | hep-th math.QA | | Abstract: | We construct and classify topological lattice field theories in three dimensions. After defining a general class of local lattice field theories, we impose invariance under arbitrary topology-preserving deformations of the underlying lattice, which are generated by two new local lattice moves. Invariant solutions are in one--to--one correspondence with Hopf algebras satisfying a certain constraint. As an example, we study in detail the topological lattice field theory corresponding to the Hopf algebra based on the group ring $C[G]$, and show that it is equivalent to lattice gauge theory at zero coupling, and to the Ponzano--Regge theory for $G=$SU(2). | | Source: | arXiv, hep-th/9305080 | | Services: | Forum | Review | PDF | Favorites | |
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