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Paper   IPM / Physic / 6527
School of Physics
  Title:   Lattice Topological Field Theory on Nonorientable Surfaces
1.  V. Karimipour
2.  A. Mostafazadeh
  Status:   Published
  Journal: J. Math. Phys.
  No.:  27
  Vol.:  38
  Year:  1997
  Pages:   49-66
  Supported by:  IPM
The lattice definition of the two-dimensional topological quantum field theory [Fukuma et al., Commun. Math. Phys. 161, 157 (1994)] is generalized to arbitrary (not necessarily orientable) compact surfaces. It is shown that there is a one-to-one correspondence between real associative *-algebras and the topological state sum invariants defined on such surfaces. The partition and n-point functions on all two-dimensional surfaces (connected sums of the Klein bottle or projective plane and g-tori) are defined and computed for arbitary *-algebras in general, and for the group ring A=\BbbR[G] of discrete groups G, in particular.

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