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arXiv · hep-th/9405108

State Sum Models and Simplicial Cohomology

Danny Birmingham·Mark Rakowski
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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 $RP^{3} \times S^{1}$, we establish that the theory has a quantum Hilbert space which differs from the classical one.

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Danny Birmingham, Mark Rakowski. 1994-09-29. State Sum Models and Simplicial Cohomology. https://doi.org/10.1007/bf02100184

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