Dirac-like Affine Fields in 3D

A generalization of the Dirac field equation in three-dimensional Minkowski space-time to the case of the $\bar{SL}(3,R)$ $\subset$ $\bar{SA}(3,R)$ symmetry is considered. Constraints that ensure a correct physical interpretation of the corresponding particle states are presented. Dirac-like equations based on both multiplicity-free and generic infinite-component $\bar{SL}(3,R)$ representations are outlined.