Geodesic
Infrared extensions of the quadratic form of the ground state of scalar field theory
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 27, Tome 494 (2020), pp. 64-74 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

We extend the quadratic forms of the Gaussian functionals of the free quantum scalar field theory to the set of functions decreasing in the infinity as $ |\vec{x}|^{-1} $. We use the momentum-space representation (after the Fourrier transform) and as the scalar product we take the product generated by the quadratic form of the Laplace operator (potential term of the quantum Hamiltonian). 
@article{ZNSL_2020_494_a3,
     author = {T. A. Bolokhov},
     title = {Infrared extensions of the quadratic form of the ground state of scalar field theory},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {64--74},
     year = {2020},
     volume = {494},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_494_a3/}
}
TY  - JOUR
AU  - T. A. Bolokhov
TI  - Infrared extensions of the quadratic form of the ground state of scalar field theory
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2020
SP  - 64
EP  - 74
VL  - 494
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2020_494_a3/
LA  - ru
ID  - ZNSL_2020_494_a3
ER  - 
%0 Journal Article
%A T. A. Bolokhov
%T Infrared extensions of the quadratic form of the ground state of scalar field theory
%J Zapiski Nauchnykh Seminarov POMI
%D 2020
%P 64-74
%V 494
%U http://geodesic.mathdoc.fr/item/ZNSL_2020_494_a3/
%G ru
%F ZNSL_2020_494_a3
T. A. Bolokhov. Infrared extensions of the quadratic form of the ground state of scalar field theory. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 27, Tome 494 (2020), pp. 64-74. http://geodesic.mathdoc.fr/item/ZNSL_2020_494_a3/

[1] R. Jackiw, “Functional representations for quantized fields”, Asia Pacific Conf. 1987:0003, Seoul Sympos. 1987:0001, Contr. to: 1st Asia Pacific Conference on High-energy Physics: Superstrings, Anomalies and Field Theory | MR

[2] M. Luscher, “Schrödinger representation in quantum field theory”, Nucl. Phys. B, 254 (1985), 52–57 | DOI | MR

[3] S. Albeverio, P. Kurasov, Singular perturbation of differential operators. Solvable Schrödinger type operators, Cambridge University Press, 2000 | MR

[4] F. A. Berezin, L. D. Faddeev, “Zamechanie ob uravnenii Shredingera s singulyarnym potentsialom”, Doklady AN SSSR, 137:5 (1961), 1011–1014 | Zbl

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

[6] L. D. Faddeev, “Zamechaniya o raskhodimostyakh i razmernoi transmutatsii v teorii Yanga-Millsa”, Teor. Mat. Fiz., 148 (2006), 133 | Zbl