CLASSICAL SOLUTION OF 2-DIMENSIONAL R(2)-GRAVITY AND CROSS-OVER PHENOMENON

Two dimensional quantum R(2)-gravity and its phase structure are exami ned in the semiclassical approach and compared with the results of the numerical simulation, Three phases are succinctly characterized by th e effective action. A classical solution of the R(2)-Liouville equatio n is obtained by use of the solution of the ordinary Liouville equatio n, The partition function is obtained analytically. A total derivative term (surface term) plays an important role there. It is shown that t he classical solution can sufficiently account for the cross-over tran sition of the surface property seen in the numerical simulation.