Even and odd symplectic and Kahlerian structures on projective superspaces

Khudaverdian, O.M.; Nersessian, A.P.

doi:10.1063/1.530320

Even and odd symplectic and Kahlerian structures on projective superspaces

O.M. Khudaverdian
(
- Yerevan State U.
)
,
A.P. Nersessian
(
- Dubna, JINR
)

Oct 30, 1992

17 pages

Published in:

J.Math.Phys. 34 (1993) 5533-5548

e-Print:

hep-th/9210091 [hep-th]

DOI:

10.1063/1.530320

Report number:

JINR-E2-92-411

View in:

reference search20 citations

Citations per year

Abstract: (arXiv)

Supergeneralization of \DC P(N) provided by even and odd K\'ahlerian structures from Hamiltonian reduction are construct.Operator

\Delta

which used in Batalin-- Vilkovisky quantization formalism and mechanics which are bi-Hamiltonian under corresponding even and odd Poisson brackets are considered.

quantization: Batalin-Vilkovisky
supersymmetry: superspace
space-time: Kaehler
differential forms: symplectic
Hamiltonian formalism
operator: algebra

References(23)

Figures(0)

[1]

D Dordrecht, 1986 Voronov T.- Geometric Integration Theory on Supermanifolds

Beresin F.A.- Introduction to Superanalysis

- Sov.Sci.Rev.C 9 1992

[2]

Gauge Algebra and Quantization

- Phys.Lett.B 102 (1981) 27-31,
- In *Moscow 1981, Proceedings, Quantum Gravity*, 463-480
•
DOI:
- 10.1016/0370-2693(81)90205-7

[3]

Closure of the Gauge Algebra, Generalized Lie Equations and Feynman Rules

- Nucl.Phys.B 234 (1984) 106-124
•
DOI:
- 10.1016/0550-3213(84)90227-X

[4]

A Note on the Antibracket Formalism

Edward Witten
(
- Princeton, Inst. Advanced Study
)

- Mod.Phys.Lett.A 5 (1990) 487
•
DOI:
- 10.1142/S0217732390000561

[5]

On background independent open string field theory

Edward Witten
(
- Princeton, Inst. Advanced Study
)

- Phys.Rev.D 46 (1992) 5467-5473
•
e-Print:
- hep-th/9208027
•
DOI:
- 10.1103/PhysRevD.46.5467

[6]

Volkov D.V

- JETP Lett. 38 (1983) 508

[7]

On Classical and Quantal Hamiltonian Systems With an Odd Poisson Bracket. (In Russian)

- Yad.Fiz. 44 (1986) 810-820,
- Yad. Fiz. 44 ( 1986) 810-820

[8]

Hamiltonian Systems With Even and Odd Poisson Brackets. Duality of Their Conservation Laws

- JETP Lett. 44 (1986) 70-72,
- Pisma Zh.Eksp.Teor.Fiz. 44 (1986) 55-57,
- Pisma Zh. Eksp. Teor. Fiz. 44 ( 1986) 55-57

[9]

On Quantization of Dynamical Systems With an Odd Poisson Bracket. (In Russian)

D.V. Volkov
(
- Kharkov, KIPT
)
,
V.A. Soroka
(
- Kharkov, KIPT
)

- Yad.Fiz. 46 (1987) 110-121

[10]

Formulation of Hamiltonian Mechanics With Even and Odd Poisson Brackets

[11]

Leites D.A.

- Dokl.Akad.Nauk Ser.Fiz. 236 (1977) 804

[12]

Shander V.N.-Dokl

- Dokl.Bulg.Akad.Nauk 36 (1983) 309

[13]

Geometry of Superspace With Even and Odd Brackets

O.M. Khudaverdian
(
- Geneva U.
)

- J.Math.Phys. 32 (1991) 1934-1937
•
DOI:
- 10.1063/1.529209

[14]

Integral Invariants of Butten's Bracket

- Lett.Math.Phys. 18 (1989) 229
•
DOI:
- 10.1007/BF00399972

[14]

Preprint of the Yerevan Phys. Inst.- 918(69)-1986

[15]

Canonical Poisson brackets of different gradings and strange superalgebras

O.M. Khudaverdian
(
- Geneva U.
)
,
A.P. Nersessian
(
- Yerevan State U.
)

- J.Math.Phys. 32 (1991) 1938-1941
•
DOI:
- 10.1063/1.529210

[15]

Preprint of Geneva University

[16]

On the geometry of supermanifolds with even and odd Kahlerian structures

A.N. Nersessian
(
- Dubna, JINR
)

- Theor.Math.Phys. 96 (1993) 866-871,
- Teor.Mat.Fiz. 96 (1993) 140-149
•
DOI:
- 10.1007/BF01074115

[17]

Supergeneralization of CP(N) as reduced phase spaces of superHamiltonian systems

- Sov. J. Contemp. Phys. 25 (1990) No. 6 23-29. (Izv. Akad. Nauk Arm. SSR 25 (1990) 330-337),
- Sov.J.Contemp.Phys. 25 (1990) 6, 23-29

[18]

Geometry., v.2, Intersciens Publishers, New York - London -Sydney, 1969

Kobayashy S.
,
Nomizu K.- Foundations of Differential

[19]

of Classical Mechanics., Nauka, Moscow, 1989

Arnold V.I.-Mathmatical Methods

[20]

Integral Invariants for Supercanonical Transformations

- Lett.Math.Phys. 5 (1981) 517-522,
- Lett. Math. Phys. 5 ( 1981) 517-522
•
DOI:
- 10.1007/BF00408133

[21]

-

Baranov M.A.
,
Schwarz A. S.

- Funct.Anal.Appl. 18 (1984) 53