Geodesic
Path integral over a $c$-number measure for interacting bosons and fermions
Teoretičeskaâ i matematičeskaâ fizika, Tome 54 (1983) no. 2, pp. 193-208 
L. F. Novikov. Path integral over a $c$-number measure for interacting bosons and fermions. Teoretičeskaâ i matematičeskaâ fizika, Tome 54 (1983) no. 2, pp. 193-208. http://geodesic.mathdoc.fr/item/TMF_1983_54_2_a3/
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     author = {L. F. Novikov},
     title = {Path integral over a~$c$-number measure for interacting bosons and fermions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {193--208},
     year = {1983},
     volume = {54},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1983_54_2_a3/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The matrix elements of the evolution operator of interacting bosons and fermions are represented as path integrals over coherent states on a Lie group. In the case of spinless electrons interacting with the electromagnetic field, this integral is transformed to an integral over the paths of the electrons in the three-dimensional space $E_3$. A scheme for constructing a path integral for electrons with spin degrees of freedom is proposed.

[1] Perelomov A. M., Commun. Math. Phys., 26:3 (1972), 222–236 | DOI | MR | Zbl

[2] Klauder J. R., Ann. Phys., 11:2 (1960), 123–168 | DOI | MR | Zbl

[3] Schweber S. S., J. Math. Phys., 3:5 (1962), 831–842 | DOI | MR | Zbl

[4] Novikov L. F., TMF, 30:2 (1977), 218–227 | MR | Zbl

[5] Klauder J. R., Phys. Rev. D, 19:8 (1979), 2349–2356 | DOI | MR

[6] Kuratsuji H., Suzuki T., Phys. Lett., 92B:1, 2 (1980), 19–22 | DOI | MR

[7] Gorokhov A. V., Teoretiko-gruppovye metody v fizike, t. I, Nauka, M., 1980, 249–256

[8] Kirillov A. A., Elementy teorii predstavleniya, Nauka, M., 1978, 343 pp. | MR | Zbl

[9] Akhiezer A. I., Berestetskii V. B., Kvantovaya elektrodinamika, Nauka, M., 1969, 623 pp. | MR

[10] Vilenkin N. Ya., Matem. sb., 75(117):3 (1968), 432–444 | MR | Zbl

[11] Gaitler V., Kvantovaya teoriya izlucheniya, IL, M., 1956, 491 pp.

[12] Veil G., Klassicheskie gruppy, ikh invarianty i predstavleniya, IL, M., 1947, 408 pp.

[13] Feinman R., Khibs A., Kvantovaya mekhanika i integraly po traektoriyam, Mir, M., 1968, 382 pp. | MR

[14] Schulman L., Phys. Rev., 176:5 (1968), 1558–1569 | DOI | MR

[15] Dowker J., J. Phys. A, 3:5 (1970), 451–461 | DOI | MR

[16] Garbaczewski P., Phys. Lett., 73A:4 (1979), 280–282 | DOI | MR

[17] Kisling D. D., J. Math. Phys., 21:6 (1980), 1460–1464 | DOI | MR

[18] Kuratsuji H., Mizobuchi Y., J. Math. Phys., 22:4 (1981), 757–764 | DOI | MR

[19] Rid M., Saimon B., Metody sovremennoi matematicheskoi fiziki, t. 2. Garmonicheskii analiz, samosopryazhennost, Mir, M., 1978, 396 pp. | MR