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arXiv · hep-th/9402144

Differential Equations for Sine-Gordon Correlation Functions at the Free Fermion Point

D. Bernard·A. Leclair
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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.

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D. Bernard, A. Leclair. 1997-03-06. Differential Equations for Sine-Gordon Correlation Functions at the Free Fermion Point. https://doi.org/10.1016/0550-3213(94)90020-5

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