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In the framework of the Symanzik approach model of the interaction of the Dirac spinor field with the material plane in the 3 + 1-dimensional space is constructed. The model contains eight real parameters characterizing the properties of the material plane. The general solution of the Euler-Lagrange equations of the model and dispersion equations for bound states are analyzed. It is shown that there is a choice of parameters of the model in which the connected states are characterized by dispersion law of a mass-less particle moving along the material plane with the dimensionless Fermi velocity not exceeding one

Bound states in a model of interaction of Dirac field with material plane