# Second order guiding-center Vlasovâ€“Maxwell equations

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In the reduced phase space of electromagnetism, the generator of duality rotations in the usual Poisson bracket is shown to generate Maxwellâ€™s equations in a second, much simpler Poisson bracket. This gives rise to a hierarchy of bi-Hamiltonian evolution equations in the standard way. The...

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An isothermal truncation of the electromagnetic gyrofluid model of Snyder and Hammett [Phys. Plasmas 8, 3199 (2001)] is shown to be Hamiltonian. The corresponding noncanonical Lieâ€“Poisson bracket and its Casimir invariants are presented. The invariants are used to obtain a set of coupled...

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The algebraic product of quantum mechanics is defined as the ordinary multiplication followed by the application of superoperator that orders the involved operators, with the symmetrization of operators that coincides with the Weyl ordering rule. Using this product, the algebra of observables is...

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A classification of compatible Lie-Poisson brackets on e*(3) is constructed. The corresponding bi-Hamiltonian systems are the classical integrable cases of the Euler-Poisson and Kirchhoff equations which describe the motion of a solid body. Bibliography: 12 titles.

- Poisson Structure and Action-Angle Variables for the Camassa—Holm Equation. Constantin, Adrian; Ivanov, Rossen // Letters in Mathematical Physics;Apr2006, Vol. 76 Issue 1, p93
The Poisson brackets for the scattering data of the Camassa-Holm equation are computed. Consequently, the action-angle variables are expressed in terms of the scattering data.

- Form-invariant Poisson brackets of hydrodynamic type with several spatial variables. Bogoyavlenskij, O.; Reynolds, P. // Journal of Mathematical Physics;May2008, Vol. 49 Issue 5, p053520
Form-invariant Poisson brackets of hydrodynamic type with several spatial variables x1,...,xp are introduced for any commuting vector fields U1,...,Um on a manifold Mn. The incompressibility equation for certain parameters of the Poisson brackets is derived. Poisson brackets connected with an...

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We construct C-algebras for a class of surfaces that are inverse images of certain polynomials of arbitrary degree. By using the directed graph associated with a matrix, the representation theory can be understood in terms of â€œloopâ€ and â€œstringâ€ representations, which are...

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Hamiltonian n-dimensional Lotkaâ€“Volterra systems are introduced that have n-1 conserved quantities. The explicit integrability in quadratures is demonstrated.

- Strict Quantizations of Almost Poisson Manifolds. Li, Hanfeng // Communications in Mathematical Physics;Aug2005, Vol. 257 Issue 3, p257
We show the existence of (non-Hermitian) strict quantization for every almost Poisson manifold.