Time-dependent correlation function of the Jordan-Wigner operator as a   Fredholm determinant
  We calculate a correlation function of the Jordan-Wigner operator in a class of free-fermion models formulated on an infinite one-dimensional lattice. We represent this function in terms of the determinant of an integrable Fredholm operator, convenient for analytic and numerical investigations. By using Wick's theorem, we avoid the form-factor summation customarily used in literature for treating similar problems. 
M. B. Zvonarev, V. V. Cheianov, T. Giamarchi