  After summarizing basic concepts for the exterior algebra we firstly discuss
the gauge structure of the bundle over base manifold for deciding the form of
the gravitational sector of the total Lagrangian in any dimensions. Then we
couple minimally a Dirac spinor field to our gravitational Lagrangian 2-form
which is quadratic in the nonmetricity and both linear and quadratic in the
curvature in two dimensions. Subsequently we obtain field equations by varying
the total Lagrangian with respect to the independent variables. Finally we find
some classes of solutions of the vacuum theory and then a solution of the Dirac
equation in a specific background and analyse them.
