DIFFERENTIAL-EQUATIONS FOR SINE-GORDON CORRELATION-FUNCTIONS AT THE FREE FERMION POINT

We demonstrate that for the sine-Gordon theory at the free fermion point, the 2-point correlation functions of the fields e(ialphaphi) for 0 < alpha < 1 can be parameterized in terms of a solution to the sinh-Gordon equation. This result is derived by summing over intermediate multiparticle states and using the form factors to express this as a Fredholm determinant. The proof of the differential equations relies on a Z2 graded multiplication law satisfied by the integral operators of the Fredholm determinant. Using this methodology, we give a new proof of the differential equations which govern the spin and disorder field correlators in the Ising model.