Geodesic
Correlation functions of two $3$-dimensional transverse potentials with power singularities
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 30, Tome 532 (2024), pp. 109-118 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

We study convolutions of two localized transverse potentials with $-5/2$-power singularities with the Green function of the Laplace operator in the $3$-dimensional space. These potentials correspond to the electromagnetic field with $-1/2$-power singularities which resides at a minimum distance to the domain of the quadratic form of the Laplacian, but does not belong to the latter. The discussed correlation functions can be used as the Nevanlinna functions for the closable extensions of quadratic form of the Laplace operator for the electromagnetic field with $-1/2$-power singularities, and in this way they are important for studying of perturbed Hamiltonians. 
@article{ZNSL_2024_532_a4,
     author = {T. A. Bolokhov},
     title = {Correlation functions of two $3$-dimensional transverse potentials with power singularities},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {109--118},
     year = {2024},
     volume = {532},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2024_532_a4/}
}
TY  - JOUR
AU  - T. A. Bolokhov
TI  - Correlation functions of two $3$-dimensional transverse potentials with power singularities
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2024
SP  - 109
EP  - 118
VL  - 532
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2024_532_a4/
LA  - en
ID  - ZNSL_2024_532_a4
ER  - 
%0 Journal Article
%A T. A. Bolokhov
%T Correlation functions of two $3$-dimensional transverse potentials with power singularities
%J Zapiski Nauchnykh Seminarov POMI
%D 2024
%P 109-118
%V 532
%U http://geodesic.mathdoc.fr/item/ZNSL_2024_532_a4/
%G en
%F ZNSL_2024_532_a4
T. A. Bolokhov. Correlation functions of two $3$-dimensional transverse potentials with power singularities. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 30, Tome 532 (2024), pp. 109-118. http://geodesic.mathdoc.fr/item/ZNSL_2024_532_a4/

[1] A. Alonso, B. Simon, “The Birman–Krein–Vishik theory of selfadjoint extensions of semibounded operators”, J. Operator Theory, 4 (1980), 251–270 | MR | Zbl

[2] V. Koshmanenko, “Quadratic Forms and Linear Operators”, Singular Quadratic Forms in Perturbation Theory, Chap. 2, Springer, Dordrecht, 1999 | DOI | MR

[3] Dokl. Akad. Nauk Ser. Fiz., 137 (1961), 1011 | MR | Zbl

[4] A. Kiselev, B. Simon, “Rank one perturbations with infinitesimal coupling”, J. Funct. Anal., 130 (1995), 345–356 | DOI | MR | Zbl

[5] S. Albeverio, P. Kurasov, Singular Perturbation of Differential Operators. Solvable Schrödinger type Operators, Cambridge University Press, 2000 | MR

[6] T. A. Bolokhov, Some solutions to the eigenstate equation of free scalar quantum field theory in the Schrödinger representation, arXiv: 2403.03049

[7] F. Gesztesy, E. Tsekanovskii, On matrix-valued Herglotz functions, arXiv: funct-an/9712004

[8] L. D. Faddeev, “Notes on divergences and dimensional transmutation in Yang–Mills theory”, Theor. Math. Phys., 148 (2006), 986–994 | DOI | MR | Zbl

[9] I. S. Gradsteyn, I. M. Ryzhik, Table of Integrals, Series, and Products, 7 ed, Academic Press, 2007 | MR