Communications in Mathematical Physics

, Volume 173, Issue 1, pp 135–154 | Cite as

State sum models and simplicial cohomology

  • Danny Birmingham
  • Mark Rakowski


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 manifoldRP3×S1, we establish that the theory has a quantum Hilbert space which differs from the classical one.


Neural Network Hilbert Space Partition Function Nonlinear Dynamics Quantum Computing 
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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Danny Birmingham
    • 1
  • Mark Rakowski
    • 2
    • 3
  1. 1.Instituut voor Theoretische FysicaUniversiteit van AmsterdamAmsterdamThe Netherlands
  2. 2.School of MathematicsTrinity CollegeDublin 2Ireland
  3. 3.Dublin Institute for Advanced StudiesDublin 4Ireland

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