Geodesic
Quantization in the neighborhood of a classical solution in the theory of a Fermi field
Teoretičeskaâ i matematičeskaâ fizika, Tome 75 (1988) no. 2, pp. 218-225 
K. A. Sveshnikov. Quantization in the neighborhood of a classical solution in the theory of a Fermi field. Teoretičeskaâ i matematičeskaâ fizika, Tome 75 (1988) no. 2, pp. 218-225. http://geodesic.mathdoc.fr/item/TMF_1988_75_2_a5/
@article{TMF_1988_75_2_a5,
     author = {K. A. Sveshnikov},
     title = {Quantization in the neighborhood of a~classical solution in the theory of {a~Fermi} field},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {218--225},
     year = {1988},
     volume = {75},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1988_75_2_a5/}
}
TY  - JOUR
AU  - K. A. Sveshnikov
TI  - Quantization in the neighborhood of a classical solution in the theory of a Fermi field
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1988
SP  - 218
EP  - 225
VL  - 75
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1988_75_2_a5/
LA  - ru
ID  - TMF_1988_75_2_a5
ER  - 
%0 Journal Article
%A K. A. Sveshnikov
%T Quantization in the neighborhood of a classical solution in the theory of a Fermi field
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1988
%P 218-225
%V 75
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1988_75_2_a5/
%G ru
%F TMF_1988_75_2_a5

Voir la notice de l'article provenant de la source Math-Net.Ru

The quantization of a Fermi–Bose field system in the neighborhood of a classical solution of the equations of motion that contains both bosonic and spinor components is considered. The latter is regarded as an absolutely anticommuting (Grassmann) component of a fermion field. On account of the transport of the fermion number, such an object mixes the fermionic and bosonic and fermionic and antifermionic degrees of freedom already at the level of the single-particle states (in the approximation of quadratic forms). Explicit expressions are obtained for the operator of the $S$ matrix, which describes such transport processes, and the total Hamiltonian and total fermion charge of the system in this approximation.

[1] Radzharaman R., Solitony i instantony, Mir, M., 1985

[2] Daschen R. F., Hasslacher B., Neveu A., Phys. Rev. D, 12:10 (1975), 2443 ; Friedberg R., Lee T. D., Phys. Rev. D, 15:5 (1977), 1694 | DOI | MR | DOI | MR

[3] Bardeen W. A., Chanowitz M. S., Drell S. D., Weinstein M., Yan T. M., Phys. Rev. D, 11:5 (1975), 1094 ; Дорохов А. Е., ТМФ, 61:1 (1984), 64–84 | DOI | MR

[4] Nadkarni S., Nielsen H. B., Zahed I., Nucl. Phys., B253 (1985), 308 | DOI

[5] Garbaczewski P., Nucl. Phys., B218:2 (1983), 332 ; J. Math. Phys., 26:3 (1985), 490–499 | MR | DOI | MR

[6] Aratyn H., Nucl. Phys., B227:1 (1983), 172–188 | DOI | MR

[7] Jackiw R., Rebbi C., Phys. Rev. D, 13:12 (1976), 3398–3410 | DOI | MR

[8] Bogolyubov N. N., UMZh, 2:2 (1950), 3–24 ; Избранные труды, т. 2, Наукова думка, Киев, 1970, С. 499–519. ; Khrustalev O. A., Razumov A. V., Taranov A. Yu., Nucl. Phys., B172 (1980), 44 | MR | Zbl | MR | Zbl | DOI | MR

[9] Sveshnikov K. A., TMF, 55:3 (1983), 361–384 | MR

[10] Sveshnikov K. A., TMF, 74:3 (1988), 373–391 | MR