  The quantisation of the two-dimensional Liouville field theory is
investigated using the path integral, on the sphere, in the large radius limit.
The general form of the $N$-point functions of vertex operators is found and
the three-point function is derived explicitly. In previous work it was
inferred that the three-point function should possess a two-dimensional lattice
of poles in the parameter space (as opposed to a one-dimensional lattice one
would expect from the standard Liouville potential). Here we argue that the
two-dimensionality of the lattice has its origin in the duality of the quantum
mechanical Liouville states and we incorporate this duality into the path
integral by using a two-exponential potential. Contrary to what one might
expect, this does not violate conformal invariance; and has the great advantage
of producing the two-dimensional lattice in a natural way.
