  A result from Palmer, Beatty and Tracy suggests that the two-point function
of certain spinless scaling fields in a free Dirac theory on the Poincare disk
can be described in terms of Painleve VI transcendents. We complete and verify
this description by fixing the integration constants in the Painleve VI
transcendent describing the two-point function, and by calculating directly in
a Dirac theory on the Poincare disk the long distance expansion of this
two-point function and the relative normalization of its long and short
distance asymptotics. The long distance expansion is obtained by developing the
curved-space analogue of a form factor expansion, and the relative
normalization is obtained by calculating the one-point function of the scaling
fields in question. The long distance expansion in fact provides part of the
solution to the connection problem associated with the Painleve VI equation
involved. Calculations are done using the formalism of angular quantization.
