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After summarizing basic concepts for the exterior algebra we firstly discussthe gauge structure of the bundle over base manifold for deciding the form ofthe gravitational sector of the total Lagrangian in any dimensions. Then wecouple minimally a Dirac spinor field to our gravitational Lagrangian 2-formwhich is quadratic in the nonmetricity and both linear and quadratic in thecurvature in two dimensions. Subsequently we obtain field equations by varyingthe total Lagrangian with respect to the independent variables. Finally we findsome classes of solutions of the vacuum theory and then a solution of the Diracequation in a specific background and analyse them.

A modified gravity model coupled to a Dirac field in 2D spacetimes with quadratic nonmetricity and curvature