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

Non-singular screw dislocations as the Coulomb gas with smoothed out coupling and the renormalization of the shear modulus