A description of $\alpha$- and $\beta$-relaxation in supercooled liquids within the framework of the continuous theory of defects

Supercooled liquid is described in terms of the theory of defected states of bond orientational order using the continuous theory of defects. It is shown that the initiation of a local orientation order leads to the breakdown of the initial SO(3) symmetry of the theory, as a result the plastic deformation fields of the linear defects become Abelian. The expressions for linear dislocation and disclination tensor potentials are derived within the framework of the quasistationary adiabatic approximation. It is shown that $\alpha$-relaxation and $\beta$-relaxation of supercooled liquid can be described as relaxation processes in the disclination and dislocation subsystems accordingly. Disclination topological moment is proposed to use as an order parameter at the description of glass transition.