Geodesic
Localization of the essential spectrum of the energy operators of $n$-particle quantum systems in a magnetic field
Teoretičeskaâ i matematičeskaâ fizika, Tome 97 (1993) no. 1, pp. 94-112 
S. A. Vugal'ter; G. M. Zhislin. Localization of the essential spectrum of the energy operators of $n$-particle quantum systems in a magnetic field. Teoretičeskaâ i matematičeskaâ fizika, Tome 97 (1993) no. 1, pp. 94-112. http://geodesic.mathdoc.fr/item/TMF_1993_97_1_a6/
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     title = {Localization of the essential spectrum of the energy operators of $n$-particle quantum systems in a~magnetic field},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Theorems on the localization of the essential spectrum of given $SO(2)$ symmetry for $n$-particle Hamiltonians in an external magnetic field are proved. The energy operators are studied for systems of arbitrary particles in the absence of an external potential field and for systems of identical particles in an external potential field. Some of the results were announced in earlier papers [1, 2].

[1] Vugalter S. A., Zhislin G. M., Funkts. analiz i ego prilozh., 25:4 (1991), 83–86 | MR | Zbl

[2] Vugalter S. A., Zhislin G. M., DAN SSSR, 317:6 (1991), 1365–1369 | MR

[3] Avron J. E., Herbert J. W., Simon B., Ann. Phys., 114 (1978), 431 | DOI | MR | Zbl

[4] Rid M., Saimon B., Metody sovremennoi matematicheskoi fiziki. Analiz operatorov, Mir, M., 1982 | MR

[5] Vugalter S. A., Zhislin G. M., Algebra i analiz, 3:6 (1991), 119–154 | MR | Zbl

[6] Antonets M. A., Zhislin G. M., Shereshevskii I. A., “O diskretnom spektre $N$-chastichnykh gamiltonianov”, prilozhenie k kn.: Iorgens K., Vaidman I., Spektralnye svoistva gamiltonovykh operatorov, Mir, M., 1976 | MR

[7] Avron J. E., Herbert J. W., Simon B., Duke, Math. J., 45 (1978), 847 | MR | Zbl

[8] Sigalov A. G., Sigal I. M., TMF, 5:1 (1970), 73–93 | MR

[9] Vugalter S. A., Zhislin G. M., TMF, 55:1 (1983), 66–77 | MR

[10] Vugal'ter S. A., Zhislin G. M., ROMP, 19:1 (1984), 39–90 | MR | Zbl