  Concise and powerful mathematical descriptions of the interplay of spin and
charge degrees of degrees of freedom with crystal lattice fluctuations are of
extreme importance in materials science. Such descriptions allow structured
approaches to optimizing material efficiencies resulting in considerable
resource savings and higher performance devices. In this work, by re-imagining
the the Gell-Mann matrices as 3$\times$3 linear transformations acting on a
column vector of position states, an SU(3) theory of the interplay between
lattice fluctuations and strong electron correlations in 2-dimensional
hexagonal materials such as graphene is formulated.
