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 2point correlation functions of the fields exp(iαΦ) for 0 < α < 1 can be parameterized in terms of a solution to a sinh-Gordon-like 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 Z 2 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. 2/97