THE RELATION BETWEEN MIXED BOUNDARY STATES IN 2-MATRIX AND 3-MATRIX MODELS

We discuss the relations among some disk amplitudes with non-trivial b oundary conditions in two-dimensional quantum gravity. These disk ampl itudes are obtained by the two-matrix model as well as the three-matri x model for the case of the tri-critical Ising model. We examine them for simple spin configurations, and find that a finite number of inser tions of different spin states cannot be observed in the continuum lim it. We also find a closed set of eight Schwinger-Dyson equations which determines the disk amplitudes in the three-matrix model.