Symplectic Reduction for Cotangent Groupoids

远莉 戴

doi:10.12677/pm.2021.113043

Symplectic Reduction of the Minimally Coupled Massless Superparticle in D=10

Differential Geometric Methods in Theoretical Physics - NATO ASI Series ◽

10.1007/978-1-4684-9148-7_68 ◽

1990 ◽

pp. 693-701

Author(s):

John Harnad ◽

Joel A. Shapiro ◽

Steven Shnider ◽

Cyrus C. Taylor

Keyword(s):

Symplectic Reduction

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Non-Holonomic Systems with Symmetry Allowing a Conformally Symplectic Reduction

New Advances in Celestial Mechanics and Hamiltonian Systems ◽

10.1007/978-1-4419-9058-7_15 ◽

2004 ◽

pp. 239-252

Author(s):

Pedro de M. Rios ◽

Jair Koiller

Keyword(s):

Symplectic Reduction ◽

Holonomic Systems

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An Example of Algebraic Symplectic Reduction for the Additive Group

Trends in Mathematics - New Trends in Analysis and Interdisciplinary Applications ◽

10.1007/978-3-319-48812-7_5 ◽

2017 ◽

pp. 35-42

Author(s):

Victoria Hoskins

Keyword(s):

Additive Group ◽

Symplectic Reduction

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Equivariant Differential Characters and Symplectic Reduction

Communications in Mathematical Physics ◽

10.1007/s00220-009-0749-9 ◽

2009 ◽

Vol 289 (2) ◽

pp. 777-801 ◽

Cited By ~ 2

Author(s):

Eugene Lerman ◽

Anton Malkin

Keyword(s):

Symplectic Reduction ◽

Differential Characters

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GENERALIZED MIURA TRANSFORMATIONS, TWO-BOSON KP HIERARCHIES AND THEIR REDUCTION TO KdV HIERARCHIES

Modern Physics Letters A ◽

10.1142/s0217732393002038 ◽

1993 ◽

Vol 08 (32) ◽

pp. 3079-3091 ◽

Cited By ~ 3

Author(s):

H. ARATYN ◽

L. A. FERREIRA ◽

J. F. GOMES ◽

R. T. MEDEIROS ◽

A. H. ZIMERMAN

Keyword(s):

Symplectic Reduction ◽

Gauge Equivalence ◽

Miura Transformations ◽

Dirac Constraints

Bracket preserving gauge equivalence is established between several two-boson generated KP type of hierarchies. These KP hierarchies reduce under symplectic reduction (via Dirac constraints) to KdV, mKdV and Schwarzian KdV hierarchies. Under this reduction the gauge equivalence takes the form of the conventional Miura maps between the above KdV type of hierarchies.

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Periodic orbits of Hamiltonian systems and symplectic reduction

Journal of Physics A General Physics ◽

10.1088/0305-4470/29/3/018 ◽

1996 ◽

Vol 29 (3) ◽

pp. 675-687 ◽

Cited By ~ 2

Author(s):

A Ibort ◽

C Martínez Ontalba

Keyword(s):

Periodic Orbits ◽

Hamiltonian Systems ◽

Symplectic Reduction

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Symplectic Reduction. Geometric Quantization. Constrained Mechanical Systems

Hamiltonian Mechanical Systems and Geometric Quantization ◽

10.1007/978-94-011-1992-4_9 ◽

1993 ◽

pp. 236-249

Author(s):

Mircea Puta

Keyword(s):

Geometric Quantization ◽

Mechanical Systems ◽

Symplectic Reduction ◽

Constrained Mechanical Systems

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ON SYMPLECTIC REDUCTION IN CLASSICAL MECHANICS

Philosophy of Physics ◽

10.1016/b978-044451560-5/50004-x ◽

2007 ◽

pp. 1-131 ◽

Cited By ~ 6

Author(s):

J. Butterfield

Keyword(s):

Classical Mechanics ◽

Symplectic Reduction

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Toeplitz Quantization and Symplectic Reduction

Differential Geometry and Physics ◽

10.1142/9789812772527_0029 ◽

2006 ◽

Author(s):

Xiaonan Ma ◽

Weiping Zhang

Keyword(s):

Symplectic Reduction

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Holstein–Primakoff Realizations on Coadjoint Orbits

Modern Physics Letters A ◽

10.1142/s0217732397000169 ◽

1997 ◽

Vol 12 (03) ◽

pp. 163-172 ◽

Cited By ~ 4

Author(s):

Phillial Oh ◽

Chaiho Rim

Keyword(s):

Symplectic Reduction ◽

Coadjoint Orbits ◽

Constrained System ◽

Normal Ordering

We derive the Holstein–Primakoff oscillator realization on the coadjoint orbits of the SU (N+1) and SU (1,N) group by treating the coadjoint orbits as a constrained system and performing the symplectic reduction. By using the action-angle variables transformations, we transform the original variables into Darboux variables. The Holstein–Primakoff expressions emerge after quantization in a canonical manner with a suitable normal ordering. The corresponding Dyson realizations are also obtained and some related issues are discussed.

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