Gauge-translational theory of dislocations with finite-sized cores and renormalization of elastic moduli

After geometric preliminaries, a gauge-translational field theory is developed which enables the dislocations with finite-sized cores in elastic body. Self-energy of the dislocation cores is accounted for by means of the translational part of the Riemann-Cartan gauge Lagrangian. The Hilbert-Einstein gauge equation plays the role of non-conventional incompatibility law. The partition function of straight screw dislocations is written in the path integration form, and the steepest descent approximation results in the dislocations with finite- sized core. The representation of two-dimensional Coulomb gas with smoothed-out coupling enables to calculate the stress-stress correlation functions. Renormalization of the shear modulus caused by the proliferation of dipoles of screw dislocations is considered. Implications are demonstrated for the shear modulus near the melting transition which are due to the singularityless character of the dislocations.