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Zap. Nauchn. Sem. POMI, 2017, Volume 465, Pages 46–60 (Mi znsl6530)  

Homogeneous extensions of the quadratic form of Laplace operator for the field interacting with two point-like particles

T. A. Bolokhov

St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia

Abstract: We consider the set of the closed homogeneous extensions of the quadratic form of Laplace operator, generated by interaction with two point-like sources. We show that this set consists of the trivial (maximal) extension, one point and the subset equivalent to the Riemann sphere.

Key words and phrases: quadratic form, Laplace operator, point-like interaction, self-adjoint extensions of symmetric operators.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-03148
17-01-00283


Full text: PDF file (218 kB)
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Document Type: Article
UDC: 517.9
Received: 29.11.2017

Citation: T. A. Bolokhov, “Homogeneous extensions of the quadratic form of Laplace operator for the field interacting with two point-like particles”, Questions of quantum field theory and statistical physics. Part 24, Zap. Nauchn. Sem. POMI, 465, POMI, St. Petersburg, 2017, 46–60

Citation in format AMSBIB
\Bibitem{Bol17}
\by T.~A.~Bolokhov
\paper Homogeneous extensions of the quadratic form of Laplace operator for the field interacting with two point-like particles
\inbook Questions of quantum field theory and statistical physics. Part~24
\serial Zap. Nauchn. Sem. POMI
\yr 2017
\vol 465
\pages 46--60
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6530}


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