

Seminar of the Department of Theoretical Physics, Steklov Mathematical Institute of RAS
March 28, 2018 14:00, Moscow, Steklov Mathematical Institute of RAS, Room 404 (8 Gubkina)






Extensions of the quadratic form of Laplace operator and the singular
perturbations of Schrodinger operator on the transverse subspace
T. A. Bolokhov^{} ^{} St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences

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Abstract:
The problem of the interaction of scalar quantum particle with
pointlike 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 3dimensional 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.

