State Sum Models and Simplicial Cohomology

Details State Sum Models and Simplicial Cohomology State Sum Models and Simplicial Cohomology

1994-05-17

arxiv.org/abs/hep-th/9405108v2

Commun.Math.Phys. 173 (1995) 135-154

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1007/BF02100184

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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