Regularization of the equations of the quantum theory for a scalar neutral field with selfinteraction in the case of two spatial degrees of freedom

The method developed earlier [1] is applied to the more complicated case of two spatial coordinates. The equations for the ground and excited states are of the same form as in the one-dimensional case, but the integrations are substituted by double ones. The divergencies more complicated than those in the one-dimensional case arise. However they can be avoided by means of extracting a certain special factor from the eigen-functional $\Omega$ of the energy operator $H$.