Abstract
We study a class of subdivision invariant lattice models based on the gauge groupZ 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 manifoldRP 3×S 1, we establish that the theory has a quantum Hilbert space which differs from the classical one.
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Communicated by G. Felder
Supported by Stichting voor Fundamenteel Onderzoek der Materie (FOM)
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Birmingham, D., Rakowski, M. State sum models and simplicial cohomology. Commun.Math. Phys. 173, 135–154 (1995). https://doi.org/10.1007/BF02100184
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DOI: https://doi.org/10.1007/BF02100184