Geodesic
Hamiltonian dynamical systems with even and odd Poisson brackets
Teoretičeskaâ i matematičeskaâ fizika, Tome 79 (1989) no. 1, pp. 117-126 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Using the example of the supersymmetric Witten mechanics we prove that the Hamiltonian systems with equal number of Grassmann even and Grassmann odd canonical variables are inherently characterized by the odd Poisson bracket in addition to the even one. The duality between even and odd integrals of motion under the change of the Poisson brackets parity is established for such systems. 
@article{TMF_1989_79_1_a10,
     author = {D. V. Volkov and A. I. Pashnev and V. A. Soroka and V. I. Tkach},
     title = {Hamiltonian dynamical systems with even and odd {Poisson} brackets},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {117--126},
     year = {1989},
     volume = {79},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1989_79_1_a10/}
}
TY  - JOUR
AU  - D. V. Volkov
AU  - A. I. Pashnev
AU  - V. A. Soroka
AU  - V. I. Tkach
TI  - Hamiltonian dynamical systems with even and odd Poisson brackets
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1989
SP  - 117
EP  - 126
VL  - 79
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1989_79_1_a10/
LA  - ru
ID  - TMF_1989_79_1_a10
ER  - 
%0 Journal Article
%A D. V. Volkov
%A A. I. Pashnev
%A V. A. Soroka
%A V. I. Tkach
%T Hamiltonian dynamical systems with even and odd Poisson brackets
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1989
%P 117-126
%V 79
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1989_79_1_a10/
%G ru
%F TMF_1989_79_1_a10
D. V. Volkov; A. I. Pashnev; V. A. Soroka; V. I. Tkach. Hamiltonian dynamical systems with even and odd Poisson brackets. Teoretičeskaâ i matematičeskaâ fizika, Tome 79 (1989) no. 1, pp. 117-126. http://geodesic.mathdoc.fr/item/TMF_1989_79_1_a10/

[1] Berezin F. A., Vvedenie v algebru i analiz s antikommutiruyuschimi peremennymi, MGU, M., 1983 | MR

[2] Leites D. A., Teoriya supermnogoobrazii, Karel. fil. AN SSSR, Petrozavodsk, 1983 | Zbl

[3] Volkov D. V., Pisma v ZhETF, 38 (1983), 508–510

[4] Kupershmidt B. A., Lett. Math. Phys., 9 (1985), 323–330 | DOI | MR | Zbl

[5] Volkov D. V., Soroka V. A., Tkach V. I., “O superspinornoi strukture odnorodnykh superprostranstv ortosimplekticheskikh grupp”, Tr. VII Mezhdunarodnogo seminara po problemam fiziki vysokikh energii i kvantovoi teorii polya, T. I, IFVE, Protvino, 1984, 48–56

[6] Volkov D. V., Soroka V. A., Tkach V. I., “O dinamicheskikh sistemakh s graduirovannymi skobkami Puassona”, Teoretiko-gruppovye metody v fizike, Nauka, M., 1986, 175–182

[7] Volkov D. V., Soroka V. A., Tkach V. I., YaF, 44 (1986), 810–820 | MR

[8] Volkov D. V., Pashnev A. I., Soroka V. A., Tkach V. I., Pisma v ZhETF, 44 (1986), 55–57

[9] Witten E., Nucl. Phys., B188 (1981), 513–554 | DOI | MR | Zbl