  A field theory is developed for a thermodynamical description of array of
parallel non-singular screw dislocations in elastic cylinder. The partition
function of the system is considered in the functional integral form.
Self-energy of the dislocation cores is chosen in the form suggested by the
gauge-translational model of non-singular screw dislocation. It is shown that
the system of the dislocations is equivalent to the two-dimensional Coulomb
gas. The coupling potential is prevented from a short-distance divergency since
the core energies are taken into account. Two-point correlation functions of
the stress components are obtained. Renormalization of the shear modulus caused
by the presence of the dislocations is studied in the approximation of
non-interacting dislocation dipoles. It is demonstrated that the finite size of
the dislocation cores results in a modification of the renormalization law.
