1994/02/28 by D. Bernard, Denis Bernard, André LeClair +1 · 2 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Combinatorics #Differential equation #Fredholm determinant #Fredholm integral equation #Fredholm theory #Integral equation #Ising model #Mathematical analysis #Mathematical physics #Mathematics #Parameterized complexity #Physics #Physics of Superconductivity and Magnetism #Quantum mechanics #Sine #hep-th #sine-Gordon equation
paper · pdf · doi:10.1016/0550-3213(94)90020-5
published as Nucl.Phys.B426:534-558,1994; Erratum-ibid.B498:619-621,1997 · 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
openalex publication_date 1994/09/01 · arxiv created 1997/03/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 correlations in the Ising model.