Kupershmidt, B. A. Mathematical aspects of quantum fluids. III. Interior Clebsch representations and transformations of symplectic two-cocycles for 4He. (English) Zbl 0635.76135 J. Math. Phys. 27, 3064-3072 (1986). Summary: [For the former parts see the author, ibid. 26, 2754-2758 (1985; Zbl 0585.76193) and ibid. 27, 2437-2444 (1986; Zbl 0626.76128).] The symplectic two-cocycle on the semidirect product Lie algebra \(g(\times (W\oplus V\) *\(\oplus V)\) is shown to be canonically related to the dual spaces of the Lie algebras (a) \(g(\times (W\oplus (g(\times V))\) and (b) \(g(\times (W\oplus (g(\times V\) *)). 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. Cited in 1 Document MSC: 76Y05 Quantum hydrodynamics and relativistic hydrodynamics 22E70 Applications of Lie groups to the sciences; explicit representations 76T99 Multiphase and multicomponent flows 81V99 Applications of quantum theory to specific physical systems 70H05 Hamilton’s equations Keywords:quantum fluids; interior Clebsch representations; symplectic two-cocycle; semidirect product Lie algebra; dual spaces of the Lie algebras; Poisson bracket Citations:Zbl 0585.76193; Zbl 0626.76128 PDFBibTeX XMLCite \textit{B. A. Kupershmidt}, J. Math. Phys. 27, 3064--3072 (1986; Zbl 0635.76135) Full Text: DOI References: [1] Lebedev V. V., Sov. Phys. JETP 48 pp 1167– (1978) [2] DOI: 10.1016/0003-4916(80)90119-0 · doi:10.1016/0003-4916(80)90119-0 [3] DOI: 10.1016/0375-9601(82)90740-X · doi:10.1016/0375-9601(82)90740-X [4] DOI: 10.1063/1.526747 · Zbl 0585.76193 · doi:10.1063/1.526747 [5] DOI: 10.1063/1.526983 · Zbl 0626.76128 · doi:10.1063/1.526983 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.