Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1995-08-10
J.Math.Phys. 38 (1997) 49-66
Physics
High Energy Physics
High Energy Physics - Theory
Corrected Latex file, 39 pages, 28 figures available upon request
Scientific paper
10.1063/1.531830
The lattice definition of the two-dimensional topological quantum field theory [Fukuma, {\em et al}, Commun.~Math.~Phys.\ {\bf 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 arbitrary $*$-algebras in general, and for the the group ring $A=\R[G]$ of discrete groups $G$, in particular.
Karimipour Vahid
Mostafazadeh Ali
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