Regular Representations of the Generalized Heisenberg Algebra
Teoretičeskaâ i matematičeskaâ fizika, Tome 129 (2001) no. 2, pp. 219-226 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We investigate general properties of regular irreducible representations of the generalized Heisenberg algebra in an arbitrary nondegenerate weakly closed space with an indefinite metric.
@article{TMF_2001_129_2_a3,
     author = {Yu. S. Vernov and M. N. Mnatsakanova},
     title = {Regular {Representations} of the {Generalized} {Heisenberg} {Algebra}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {219--226},
     year = {2001},
     volume = {129},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2001_129_2_a3/}
}
TY  - JOUR
AU  - Yu. S. Vernov
AU  - M. N. Mnatsakanova
TI  - Regular Representations of the Generalized Heisenberg Algebra
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2001
SP  - 219
EP  - 226
VL  - 129
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2001_129_2_a3/
LA  - ru
ID  - TMF_2001_129_2_a3
ER  - 
%0 Journal Article
%A Yu. S. Vernov
%A M. N. Mnatsakanova
%T Regular Representations of the Generalized Heisenberg Algebra
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2001
%P 219-226
%V 129
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2001_129_2_a3/
%G ru
%F TMF_2001_129_2_a3
Yu. S. Vernov; M. N. Mnatsakanova. Regular Representations of the Generalized Heisenberg Algebra. Teoretičeskaâ i matematičeskaâ fizika, Tome 129 (2001) no. 2, pp. 219-226. http://geodesic.mathdoc.fr/item/TMF_2001_129_2_a3/

[1] C. R. Putnam, Commutation Properties of Hilbert Space Operators and Related Topics, Springer, Berlin–Heidelberg–New York, 1967 | MR | Zbl

[2] F. Rellich, Nach. Akad. Wiss. Gött. Math.–Phys. Klasse, 1946, 107 ; J. Dixmier, Comp. Math., 13, 1958, 263 | MR | Zbl | MR | Zbl

[3] F. Acerbi, G. Morchio, F. Strocchi, Infrared singular fields and non-regular representations of CCR algebras, Preprint SISSA 39/92/FM, 1992 ; Lett. Math. Phys., 27 (1993), 1 | MR | DOI | MR | Zbl

[4] K. Schmüdgen, J. Funct. Analysis, 50 (1983), 8 | DOI | MR | Zbl

[5] F. Strocchi and A. S. Wightman, J. Math. Phys., 15 (1974), 2198 | DOI | MR

[6] G. Morchio and F. Strocchi, Ann. Inst. Henri Poincaré, 33 (1980), 251 | MR

[7] F. Strocchi, Selected Topics on the General Properties of Quantum Field Theory, World Scientific, Singapore, 1993 | MR | Zbl

[8] M. Mnatsakanova, G. Morchio, F. Strocchi, and Yu. Vernov, J. Math. Phys., 29 (1998), 2969 | DOI | MR

[9] L. D. Faddeev, “Integrable models in $(1+1)$-dimensional quantum field theory”, Recent Advances in Field Theory and Statistical Mechanics, Les Houches, session XXXIX, eds. J.-B. Zuber and R. Stora, Elsevier, Amsterdam, 1982, 563 | MR

[10] P. P. Kulish and E. K. Sklyanin, “Quantum spectral transform method. Recent developments”, Integrable Quantum Field Theory, Proc. of the Symp. (Tvaerminne, Finland, 23–27 March, 1981), Lect. Notes Phys., 151, eds. J. Hietarinta and C. Montonen, Springer, Berlin, 1982, 61 | DOI | MR

[11] M. Chaichian and P. P. Kulish, Phys. Lett. B, 234 (1990), 72 | DOI | MR | Zbl

[12] P. P. Kulish and E. V. Damaskinsky, J. Phys. A, 23 (1990), L415 ; П. П. Кулиш, ТМФ, 86 (1991), 8 | DOI | MR | Zbl | MR

[13] M. S. Plyushchay, Nucl. Phys. B, 491 (1997), 619 | DOI | MR | Zbl

[14] M. S. Plyushchay, Mod. Phys. Lett. A, 11 (1996), 2953 | DOI | MR | Zbl

[15] M. Chaichian, M. N. Mnatsakanova, and Yu. S. Vernov, “Analogue of the von Neumann's theorem of the q-oscillator algebra”, Proc. of the XV Workshop “Problems on High Energy Physics and Field Theory” (Protvino, 1992), eds. A. P. Samokhin and G. L. Rcheulishvili, IHEP, Protvino, 1995, 126

[16] Yu. S. Vernov, M. N. Mnatsakanova, TMF, 113 (1997), 355 | DOI | MR | Zbl

[17] Yu. S. Vernov, M. N. Mnatsakanova, TMF, 125 (2000), 272 | DOI | MR | Zbl

[18] M. N. Mnatsakanova, G. Morchio, and Yu. S. Vernov, “Canonical commutation relations in a positive and an indefinite metric spaces”, Quarks-96, Proc. 9th Int. seminar. V. 2 (Yaroslavl, Russia, May 5–11, 1996), eds. V. A. Matveev, A. A. Penin, V. A. Rubakov, and A. N. Tavkhelidze, Inst. Nucl. Res., Russ. Acad. Sci, Moscow, 1997, 51