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J. Math. Phys. 27, 3064 (1986); http://dx.doi.org/10.1063/1.527237 (9 pages)
Mathematical aspects of quantum fluids. III. Interior Clebsch representations and transformations of symplectic two‐cocycles for 4He
(Received 1 May 1986; accepted 20 August 1986)
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Add to FacebookThe symplectic two‐cocycle on the semidirect product Lie algebra 
⨴(W⊕V∗⊕V) is shown to be canonically related to the dual spaces of the Lie algebras (a) ⨴(W⊕(⨴V)) and (b) ⨴(W⊕(⨴V∗)). This fact (a) explains the second Poisson bracket for irrotational 4He and (b) leads to a derivation of a new nonlinear Poisson bracket for rotating 4He.
⨴(W⊕V∗⊕V) is shown to be canonically related to the dual spaces of the Lie algebras (a) ⨴(W⊕(⨴V)) and (b) ⨴(W⊕(⨴V∗)). This fact (a) explains the second Poisson bracket for irrotational 4He and (b) leads to a derivation of a new nonlinear Poisson bracket for rotating 4He.KEYWORDS and PACS
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V. V. Lebedev and I. M. Khalatnikov, “Hamiltonian hydrodynamic equations for a quantum fluid in the presence of solitons,” Sov. Phys. JETP 48, 1167 (1978).
B. A. Kupershmidt, “Mathematical aspects of quantum fluids. I. Generalized two-cocycles of 4He type,” J. Math. Phys. 26, 2754 (1985JMAPAQ000026000011002754000001).
B. A. Kupershmidt, “Mathematical aspects of quantum fluids. II. 4He, and Clebsch representations of symplectic two-cocycles, ”J. Math. Phys. 27, 2437 (1986JMAPAQ000027000009002437000001).
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