State Sum Models and Simplicial Cohomology

Abstract

We study a class of subdivision invariant lattice models based on the gauge group $Z_p$, with particular emphasis on the four dimensional example. This model is based upon the assignment of field variables to both the $1$- and $2$-dimensional simplices of the simplicial complex. The property of subdivision invariance is achieved when the coupling parameter is quantized and the field configurations are restricted to satisfy a type of mod-$p$ flatness condition. By explicit computation of the partition function for the manifold $R{P}^3\times S^1$, we establish that the theory has a quantum Hilbert space which differs from the classical one.

28 pages, Latex, ITFA-94-13, (Expanded version with two new sections)

References in corpus (1)

• Discrete Quantum Field Theories and the Intersection Form

Cited by in corpus (8)

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• Hamiltonian models for topological phases of matter in three spatial dimensions
• 4-dimensional BF Gravity on the Lattice
• On Dijkgraaf-Witten Type Invariants
• Quasi-Topological Field Theories in Two Dimensions as Soluble Models
• Discrete Quantum Field Theories and the Intersection Form
• On two-dimensional quasitopological field theories
• Finite groups, spherical 2-categories, and 4-manifold invariants