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 eiαΦ for 0<α<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. ((orig.))