Extensions of the quadratic form of Laplace operator and the singular perturbations of Schrodinger operator on the transverse subspace

The problem of the interaction of scalar quantum particle with point-like potential, considered in 1961 by F.Berezin and L.Faddeev, can be reformulated in the terms of extensions of the quadratic form of Laplace operator. We discuss a similar problem for the case of the transverse vector field in 3-dimensional space. Using the basis of Vector Spherical Harmonics we parametrize the transverse subspace, and construct the extensions of the corresponding quadratic form produced by the vector Laplace operator. The connection between the coefficients in the resulting expression and the renormalization of the coupling constant in the original physical problem is discussed.