  Explicit factorized formulas for the matrix elements (form-factors) of the
spin operators \sigma^x and \sigma^y between the eigenvectors of the
Hamiltonian of the finite quantum periodic XY-chain in a transverse field were
derived. The derivation is based on the relations between three models: the
model of quantum XY-chain, Ising model on 2D lattice and N=2
Baxter-Bazhanov-Stroganov \tau^{(2)}-model. Due to these relations we transfer
the formulas for the form-factors of the latter model recently obtained by the
use of separation of variables method to the model of quantum XY-chain.
Hopefully, the formulas for the form-factors will help in analysis of
multipoint dynamic correlation functions at a finite temperature. As an
example, we re-derive the asymptotics of two-point correlation function in the
disordered phase without the use of the Toeplitz determinants and the
Wiener-Hopf factorization method.
