Reference-point-independent dynamics of molecular liquids and glasses in the tensorial formalism

We apply the tensorial formalism to the dynamics of molecular liquids and glasses. This formalism separates the degrees of freedom into translational and orientational ones. Using the Mori-Zwanzig projection formalism, the equations of motion for the tensorial density correlators S(lmn,l'm'n')(q-->,t) are derived. For this we show how to choose the slow variables such that the resulting Mori-Zwanzig equations are covariant under a change of the reference point of the body fixed frame. We also prove that the memory kernels obtained from mode-coupling theory (MCT) including all approximations preserve the covariance. This covariance makes, e.g., the glass transition point, the two universal scaling laws and particularly the corresponding exponents independent on the reference point and on the mass and moments of inertia, i.e., they only depend on the properties of the potential energy landscape. Finally, we show that the corresponding MCT questions for linear molecules can be obtained from those for arbitrary molecules and that they differ from earlier equations that are not covariant.