摘要: Abstract We investigate the double-scaled free fermion theory of c = 1 matrix model. compute correlation functions eigenvalue density field and compare with predictions a relativistic boson theory. The behaves as at long distances, but has softer behavior short distances. soft short-distance is closely related to breakdown topological expansion high energies. also macroscopic loop amplitudes 1, finding an integral representation for n -loop all orders perturbation evaluate integrals explicitly two, three, four loops. small length asymptotic then gives local operators in two-macroscopic-loop formula information on spectrum wave three- four-loop give scattering tachyon Again, breaks down our from Liouville