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State Sum Models and Simplicial Cohomology
High Energy Physics - Theory · Submitted 17 May 1994
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study a class of subdivision invariant lattice models based on the gauge group $Z_{p}$, with particular emphasis on the four dimensional example. | contribution 0.99 | 0.88 | 0.05 | asserted 0.88 |
| s1 | This model is based upon the assignment of field variables to both the $1$- and $2$-dimensional simplices of the simplicial complex. | method 0.92 | 0.51 | 0.03 | asserted 1.00 |
| s2 | 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. | method 0.96 | 0.47 | 0.07 | asserted 1.00 |
| s3 | 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. | result 1.00 | 0.96 | 0.65 | asserted 1.00 |
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Original 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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Examples for topological models with discrete groups are discussed for instance in [ref] .
Spin foam models with finite groups · Topological models · 0.89
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