  We introduce the notion of parafermionic fields as the chiral fields which
describe particle excitations in two-dimensional conformal field theory, and
argue that the parafermionic conformal dimensions can be determined using scale
invariant scattering theory. Together with operator product arguments this may
provide new information, in particular for non-rational conformal theories. We
obtain in this way the field theoretical derivation of the critical exponents
of the random cluster and O(n) models, which in the limit of vanishing central
charge yield percolation and self-avoiding walks. A simple derivation of the
relation between S-matrix and Lagrangian couplings of sine-Gordon model is also
given.
