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In the framework of the concept of time correlation functions, we develop aself-consistent relaxation theory of the transverse collective particledynamics in liquids. The theory agrees with well-known results in both theshort-wave (free particle dynamics) and the long-wave (hydrodynamic) limits. Weobtain a general expression for the spectral density~$C_T(k,\omega)$ oftransverse particle current realized in the range of wave numbers $k$. Indomain of microscopic spatial scales comparable to action scale of effectiveforces of interparticle interaction, the theory reproduces a transition from aregime with typical equilibrium liquid dynamics to a regime with collectiveparticle dynamics where properties similar to solid-state properties appear:effective shear stiffness and transverse (shear) acoustic waves. In theframework of the corresponding approximations, we obtain expressions for thespectral density of transverse particle current for all characteristic regimesin equilibrium collective dynamics. We obtain expressions for dispersion lawfor transverse (shear) acoustic waves and also relations for the kinematicshear viscosity $\nu$, the transverse speed of sound $v^{(T)}$, and thecorresponding sound damping coefficient $\Gamma^{(T)}$. We compare thetheoretical results with the results of atomic dynamics simulations of liquidlithium near the melting point.

Quasi-solid state microscopic dynamics in equilibrium classical liquids: Self-consisnent relaxation theory