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Paper IPM / Physic / 6527  


Abstract:  
The lattice definition of the twodimensional 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 onetoone correspondence between real associative
*algebras
and the topological state sum invariants defined on such surfaces.
The partition and npoint functions on all twodimensional surfaces
(connected sums of the Klein bottle or projective plane and
gtori) 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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