Geodesic
A Kähler structure of the triplectic geometry
Teoretičeskaâ i matematičeskaâ fizika, Tome 124 (2000) no. 3, pp. 355-372 
M. A. Grigoriev; A. M. Semikhatov. A Kähler structure of the triplectic geometry. Teoretičeskaâ i matematičeskaâ fizika, Tome 124 (2000) no. 3, pp. 355-372. http://geodesic.mathdoc.fr/item/TMF_2000_124_3_a0/
@article{TMF_2000_124_3_a0,
     author = {M. A. Grigoriev and A. M. Semikhatov},
     title = {A {K\"ahler} structure of the triplectic geometry},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {355--372},
     year = {2000},
     volume = {124},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2000_124_3_a0/}
}
TY  - JOUR
AU  - M. A. Grigoriev
AU  - A. M. Semikhatov
TI  - A Kähler structure of the triplectic geometry
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2000
SP  - 355
EP  - 372
VL  - 124
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2000_124_3_a0/
LA  - ru
ID  - TMF_2000_124_3_a0
ER  - 
%0 Journal Article
%A M. A. Grigoriev
%A A. M. Semikhatov
%T A Kähler structure of the triplectic geometry
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2000
%P 355-372
%V 124
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2000_124_3_a0/
%G ru
%F TMF_2000_124_3_a0

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

We study the geometry of the triplectic quantization of gauge theories. We show that the triplectic geometry is determined by the geometry of a Kähler manifold $\mathcal N$ endowed with a pair of transversal polarizations. The antibrackets can be brought to the canonical form if and only if $\mathcal N$ admits a flat symmetric connection that is compatible with the complex structure and the polarizations.

[1] I. A. Batalin, P. M. Lavrov, I. V. Tyutin, J. Math. Phys., 31 (1990), 1487 ; 32 (1991), 532 ; 2513 | DOI | MR | Zbl | DOI | MR | Zbl | MR

[2] C. M. Hull, Mod. Phys. Lett. A, 5 (1990), 1871 | DOI | MR | Zbl

[3] I. A. Batalin, G. A. Vilkovisky, Phys. Lett. B, 102 (1981), 27 ; Phys. Rev. D, 28 (1983), 2567 | DOI | MR | DOI | MR

[4] I. A. Batalin, R. Marnelius, Phys. Lett. B, 446 (1995), 44 | DOI | MR

[5] I. A. Batalin, R. Marnelius, A. M. Semikhatov, Nucl. Phys. B, 446 (1995), 249 | DOI | MR

[6] I. A. Batalin, R. Marnelius, Nucl. Phys. B, 465 (1996), 521 | DOI | MR | Zbl

[7] I. A. Batalin, I. V. Tyutin, Int. J. Mod. Phys. A, 8 (1993), 2333 ; Mod. Phys. Lett. A, 8 (1993), 3673 ; 9 (1994), 1707 | DOI | MR | Zbl | DOI | MR | Zbl | DOI | MR | Zbl

[8] A. Schwarz, Commun. Math. Phys., 155 (1993), 249 | DOI | MR | Zbl

[9] H. Hata, B. Zwiebach, Ann. Phys., 229 (1994), 177 | DOI | MR | Zbl

[10] A. Sen, B. Zwiebach, Commun. Math. Phys., 177 (1996), 305 | DOI | MR | Zbl

[11] A. Schwarz, Commun. Math. Phys., 158 (1993), 373 | DOI | MR

[12] M. A. Grigoriev, A. M. Semikhatov, Phys. Lett. B, 417 (1998), 259 | DOI | MR

[13] A. Nijenhuis, Indag. Math., 17 (1955), 390 | DOI | MR

[14] F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz, D. Sternheimer, Ann. Phys., 111 (1978), 61 | DOI | MR | Zbl

[15] D. B. Fuks, Kogomologii beskonechnomernykh algebr Li, Nauka, M., 1984 | MR | Zbl

[16] D. A. Leites, UMN, 35:1 (1980), 3 | MR | Zbl

[17] M. A. Grigoriev, A. M. Semikhatov, A Kaehler Structure of the Triplectic Geometry, E-print hep-th/9807023

[18] I. M. Gelfand, I. Zakharevich, Webs, Lenard schemes, and the local geometry of bihamiltonian Toda and Lax structures, E-print math.DG/9903080 | MR

[19] V. Guillemin, S. Sternberg, Geometric Asymptotics, Amer. Math. Soc., Providence, RI, 1977 | MR | Zbl