Geodesic
On the Elimination of the Stueckelberg Divergences in the Hamiltonian Field Theory
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematical physics. Problems of quantum field theory, Tome 226 (1999), pp. 112-133 Cet article a éte moissonné depuis la source Math-Net.Ru

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The Stueckelberg divergences arise in the Hamiltonian approach to quantum field theory. To eliminate these divergences, certain conditions are imposed not only on the dependence of the counterterms on the regularization parameters but also on the dependence of the initial state vector on these parameters. A class of evolution-invariant initial conditions is constructed. This class can be constructed both by the Faddeev-type transformation and by the Bogolyubov method based on the consideration of the theory with smooth switching on the interaction. These methods are illustrated by a simple example of the Stueckelberg divergences that arise when calculating the particle-decay rate and are applied to the analysis of the Hamiltonian semiclassical field theory. A condition on the initial data for the Schrödinger equation is obtained in the leading order of the complex-germ theory. 
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     author = {V. P. Maslov and O. Yu. Shvedov},
     title = {On the {Elimination} of the {Stueckelberg} {Divergences} in the {Hamiltonian} {Field} {Theory}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_1999_226_a8/}
}
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V. P. Maslov; O. Yu. Shvedov. On the Elimination of the Stueckelberg Divergences in the Hamiltonian Field Theory. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematical physics. Problems of quantum field theory, Tome 226 (1999), pp. 112-133. http://geodesic.mathdoc.fr/item/TM_1999_226_a8/

[1] Bogolyubov N. N., Shirkov D. V., Vvedenie v teoriyu kvantovannykh polei, Nauka, M., 1973 | MR | Zbl

[2] Shvarts A. S., Matematicheskie osnovy kvantovoi teorii polya, Atomizdat, M., 1975 | MR

[3] Shvarts A. S., Elementy kvantovoi teorii polya. Bozonnye vzaimodeistviya, Atomizdat, M., 1975 | MR

[4] Bogolyubov N. N., “K voprosu ob osnovnykh uravneniyakh relyativistskoi kvantovoi teorii polya”, DAN SSSR, 81:5 (1951), 757–760 | MR | Zbl

[5] Bogolyubov N. N., Logunov A. A., Oksak A. I., Todorov I. T., Obschie printsipy kvantovoi teorii polya, Nauka, M., 1987 | MR

[6] Stueckelberg E. C. G., “Relativistic quantum theory for finite time intervals”, Phys. Rev., 81 (1951), 130–133 | DOI | MR | Zbl

[7] Vaitman A., Problemy v relyativistskoi dinamike kvantovannykh polei, Nauka, M., 1968

[8] Maslov V. P., Teoriya vozmuschenii i asimptoticheskie metody, Izd-vo MGU, M., 1965

[9] Maslov V. P., Operatornye metody, Nauka, M., 1973 | MR

[10] Maslov V. P., Kompleksnyi metod VKB v nelineinykh uravneniyakh, Nauka, M., 1977 | MR

[11] Khepp K., Teoriya perenormirovok, Nauka, M., 1974 | MR

[12] Faddeev L. D., “O razdelenii effektov samodeistviya i rasseyaniya po teorii vozmuschenii”, DAN SSSR, 152:3 (1963), 573–576 | MR

[13] Shirokov M. I., “Kvantovaya elektrodinamika s vneshnim tokom i potentsialom”, Yader. fizika, 7 (1968), 672–684

[14] Slavnov A. A., Faddeev L. D., Vvedenie v kvantovuyu teoriyu kalibrovochnykh polei, Nauka, M., 1988 | MR | Zbl

[15] Berezin F. A., Metod vtorichnogo kvantovaniya, Nauka, M., 1986 | MR | Zbl

[16] Maslov V. P., Shvedov O. Yu., “O nachalnykh usloviyakh v kvaziklassicheskoi teorii polya”, TMF, 114:2 (1998), 233–249 | MR | Zbl

[17] Maslov V. P., Shvedov O. Yu., “O kompleksnom rostke v relyativistskoi teorii polya”, Dokl. RAN, 358:3 (1998), 319–322 | MR | Zbl