Symplectic Reduction for Cotangent Groupoids

2021 ◽  
Vol 11 (03) ◽  
pp. 323-329
Author(s):  
远莉 戴
Keyword(s):  
Symplectic Reduction

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

1993 ◽  
Vol 08 (32) ◽  
pp. 3079-3091 ◽  
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.

scholarly journals Holstein–Primakoff Realizations on Coadjoint Orbits

1997 ◽  
Vol 12 (03) ◽  
pp. 163-172 ◽  
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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