March 31, 1999
Various definitions of chiral observables in a given Moebius covariant two-dimensional theory are shown to be equivalent. Their representation theory in the vacuum Hilbert space of the 2D theory is studied. It shares the general characteristics of modular invariant partition functions, although SL(2,Z) transformation properties are not assumed. First steps towards classification are made.
Keywords:two-dimensional models, chiral models