Differential Equations for Sine-Gordon Correlation Functions at the Free Fermion Point
arXiv:hep-th/9402144 · doi:10.1016/0550-3213(94)90020-5
Abstract
We demonstrate that for the sine-Gordon theory at the free fermion point, the 2-point correlation functions of the fields $\exp (i\al Φ)$ for $0< \al < 1$ 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 $\Zmath_2$ 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.
28 pages. In this corrected version, more general solutions to the differential equations, which are required for correlators of inequivalent fields, are included. erratum hep-th/9703055 describes the substantial changes from original version
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