  The paper exhibits a product-to-sum formula for the observables of a certain
quantization of the moduli space of flat SU(2)-connections on the torus. This
quantization was defined using the topological quantum field theory that was
developed by Reshetikhin and Turaev from the quantum group of SL(2,C) at roots
of unity. As a corollary it is shown that the algebra of quantum observables is
a subalgebra of the noncommutative torus with rational rotation angle. The
proof uses topological quantum field theory with corners, and is based on the
description of the matrices of the observables in a canonical basis of the
Hilbert space of the quantization.
