CLASSIFICATION AND CONSTRUCTION OF UNITARY TOPOLOGICAL FIELD-THEORIES IN 2 DIMENSIONS

It is proven that unitary two-dimensional topological field theories are uniquely characterized by n positive real numbers lambda(1),...,lambda(n), which can be regarded as the eigenvalues of a Hermitian handle creation operator. The number n is the dimension of the Hilbert space associated with the circle, and the partition functions for closed surfaces have the form Z(g) = Sigma(i=1)(n) lambda(i)(g-1), where g is the genus. The eigenvalues can be arbitrary positive numbers. It is shown how such a theory can be constructed on triangulated surfaces.