Geodesic
Quantization of a particle-like classical solution in Bogoliubov variables without Dirac's brackets
Teoretičeskaâ i matematičeskaâ fizika, Tome 93 (1992) no. 3, pp. 384-402 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The Bogoliubov collective coordinate method is applied to soliton quantization in such a way that the soliton and the meson field are considered as independent canonical degrees of freedom of the system from the beginning. The quantization of the enlarged system proceeds by means of canonical rules without applying to Dirac's formalism of constrained systems. The true number of independent degrees of freedom is fixed by means of a set of additional conserved charges and corresponding symmetry relations. The role of the soliton recoil in the dynamics of the coupled system is discussed in detail. The full form of the Born amplitudes in the meson-soliton scattering is calculated directly in the Hamiltonian picture. The relations to others methods of soliton quantization are also discussed. 
@article{TMF_1992_93_3_a1,
     author = {O. A. Khrustalev and K. A. Sveshnikov},
     title = {Quantization of a~particle-like classical solution in {Bogoliubov} variables without {Dirac's} brackets},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {384--402},
     year = {1992},
     volume = {93},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TMF_1992_93_3_a1/}
}
TY  - JOUR
AU  - O. A. Khrustalev
AU  - K. A. Sveshnikov
TI  - Quantization of a particle-like classical solution in Bogoliubov variables without Dirac's brackets
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1992
SP  - 384
EP  - 402
VL  - 93
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1992_93_3_a1/
LA  - en
ID  - TMF_1992_93_3_a1
ER  - 
%0 Journal Article
%A O. A. Khrustalev
%A K. A. Sveshnikov
%T Quantization of a particle-like classical solution in Bogoliubov variables without Dirac's brackets
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1992
%P 384-402
%V 93
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1992_93_3_a1/
%G en
%F TMF_1992_93_3_a1
O. A. Khrustalev; K. A. Sveshnikov. Quantization of a particle-like classical solution in Bogoliubov variables without Dirac's brackets. Teoretičeskaâ i matematičeskaâ fizika, Tome 93 (1992) no. 3, pp. 384-402. http://geodesic.mathdoc.fr/item/TMF_1992_93_3_a1/

[1] Rajaraman R., Soiitons and Instantons, North-Holland, Amsterdam, 1982 | MR | Zbl

[2] Bogoliubov N. N., Ukr. Mat. Zh., 2 (1950), 3–20 | MR

[3] Solodovnikova E. P., Tavkhelidze A. N., Khrustalev O. A., Teor. Mat. Fiz., 10 (1972), 162–181 | DOI

[4] Razumov A. V., Khrustalev O. A., Teor. Mat. Fiz., 29:3 (1976), 300–308 ; Razumov A. V., Taranov A. Yu., Teor. Mat. Fiz., 35:3 (1978), 312–321 ; Razumov A. V., Teor. Mat. Fiz., 30:1 (1976), 18–27 | DOI | MR | DOI | MR | MR

[5] Khrustalev O. A., Razumov A. V., Taranov A. Yu., Nucl.Phys. B, 172 (1980), 44–58 | DOI | MR

[6] Gervais J.-L., Jevicki A., Sakita B., Phys. Rev. D, 12 (1975), 1038–1051 | DOI

[7] Tomboulis E., Phys. Rev. D, 12 (1975), 1678–1683 | DOI

[8] Christ N.-H., Lee T. D., Phys. Rev. D, 12 (1975), 1606–1627 | DOI | MR

[9] Adkins G., Nappi C., Witten E., Nucl. Phys. B, 223 (1983), 552–578 ; Adkins G., Nappi C., Nucl. Phys. B, 233 (1984), 109–124 | DOI | MR | DOI

[10] Zahed I., Brown G. E., Phys. Rep., 142 (1986), 1–99 | DOI | MR

[11] Dirac P. A. M., Lectures on Quantum Mechanics, Yeshiva University, New York, 1964 | MR

[12] Hosoya A., Kikkawa T., Nucl. Phys. B, 101 (1975), 271–885 ; Tomboulis E., Woo T. T., Ann. of Phys., 98 (1976), 1–13 | DOI | DOI

[13] Steinmann O., Nucl. Phys. B, 131 (1977), 459–476 ; Nucl. Phys. B, 145 (1978), 141–165 | DOI | MR | DOI | MR

[14] Semenoff G., Matsumoto H., Umezawa H., Journ. Math. Phys., 22 (1981), 2208–2223 ; Progr. Theor. Phys., 67 (1982), 1619–1636 ; Matsumoto H., Papastamatiou N. J., Semenoff G., Umezawa H., Phys. Rev. D, 24 (1981), 406–425 | DOI | MR | DOI | MR | DOI

[15] Sveshnikov K. A., Teor. Mat. Fiz., 55 (1983), 361–384 ; Theor. Math. Fiz., 74 (1988), 373–391 | DOI | MR | MR

[16] Ohta K., Phys. Lett. B, 234 (1990), 229–234 ; Ohta K., 242 (1990), 334–340 ; Phys. Rev. D, 43 (1991), 2635–2648 | DOI | DOI | DOI

[17] Uehara M., Progr. Theor. Phys., 83 (1990), 790–801 | DOI

[18] Hayashi A., Saito S., Uehara M., Phys. Lett. B, 246 (1990), 15–21 | DOI

[19] Sveshnikov K. A., A New Version of Collective Coordinate Quantization, preprint BI-TP 90/23, Bielefeld, 1990

[20] Parmentola J. A., Zahed I., Chiral Solitons, ed. K. F. Liu, World Scientific, Singapoure, 1987 | MR

[21] Daschen R., Hasslacher B., Neveu A., Phys. Rev. D, 10 (1974), 4130–4161 | DOI

[22] Verschelde H., Phys. Lett. B, 215 (1988), 444–450 ; Phys. Lett. B, 232 (1989), 15–20 ; Vershelde H., Verbeke H., Nucl. Phys. A, 495 (1989), 523–536 | DOI | DOI | DOI | MR

[23] Goldstone J., Jackiw R., Phys. Rev. D, 11 (1975), 1486–1498 ; Liang Y. G., Li B. A., Liu K. F., Su R. K., Phys. Lett. B, 243 (1990), 133–138 | DOI | DOI | MR

[24] Kawarabayashi K., Ohta K., Phys. Lett. B, 216 (1990), 205–212 | DOI | MR

[25] Gervais J.-L., Sakita B., Phys. Rev. D, 30 (1984), 1795–1806 ; Dyakonov D. I., Petrov V. Yu., Pobylitsa P. V., Phys. Lett. B, 205 (1988), 372–378 ; Liu H., Oka M., Phys. Rev. D, 40 (1989), 883–889 ; Vershelde H., Phys. Lett. B, 249 (1990), 175–180 ; Hayashi A., Saito S., Uehara M., Phys. Rev. D, 43 (1991), 1520–1531 | DOI | DOI | DOI | DOI | DOI