Lattice Topological Field Theory on Non-Orientable Surfaces
نویسنده
چکیده
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 twodimensional surfaces (connected sums of the Klein bottle or projective plane and g-tori) are defined and computed for arbitrary ∗-algebras in general, and for the the group ring A = IR[G] of discrete groups G, in particular.
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