Interaction of Tachyons and Discrete States in c=1 2-D Quantum Gravity
  The two-dimensional (2-D) quantum gravity coupled to the conformal matter with $c=1$ is studied. We obtain all the three point couplings involving tachyons and/or discrete states via operator product expansion. We find that cocycle factors are necessary and construct them explicitly. We obtain an effective action for these three point couplings. This is a brief summary of our study of couplings of tachyons and discrete states, reported at the workshop in Tokyo Metropolitan University, December 4-6, 1991. 
Yoichiro Matsumura, Norisuke Sakai, Yoshiaki Tanii