1D spin-1/2 Fermi gas with a self-interaction allows a non-perturbative solution. Using the algebraic Bethe ansatz approach eigenvectors and spectrum of the system can be written. Computation of the observables, such as transport coefficients, however still very complicated problem. The first problem, studied in this thesis, is a calculation of the form factors of the monodromy matrix, that can be used for the computation of form factor of the ultralocal operators. The correlation functions can be expressed via a form factors series. In order to perform summation of this infinity series the numerical algorithm that allows to scan the basis of the eigenstates and choose only the important contributions to the from factor sum was developed. The developed approach allows to study system at zero-temperature and can be generalised for a similar model of Bose gas and lattice supersymmetric t-J system of electron gas.
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