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In the present paper, the method for describing inhomogeneous states withlocal translational symmetry is proposed, based on the symmetry-dependentinteraction between the order parameter (OP) and compensating field in thephenomenological Landau theory. It is shown that dimensionality of thecompensating field in the extended derivative is associated with representationof the OP and does not coincide with the dimensionality of the derivativeitself. This results in the correct definition of transformational propertiesof physical fields in the local Landau theory and in the equations of continuumtheory of dislocations in the system of equations of state. The mechanism isproposed to construct the Ginzburg-Landau potential for states with localtranslational symmetry that correspond to HTS states. It is shown that minimalinteraction between the superconducting OP and tensor compensating field isresponsible for electron-phonon interaction in the BCS model.

Minimal Interaction in the Local Landau Theory and Construction of the  Phenomenological Ginzburg-Landau Potential in Terms of Electron-Phonon  Interaction