Abstract
This paper develops the theory of affine Lie–Poisson reduction and applies this process to Yang–Mills and Hall magnetohydrodynamics for fluids and superfluids. As a consequence of this approach, the associated Poisson brackets are obtained by reduction of a canonical cotangent bundle. A Kelvin–Noether circulation theorem is presented and is applied to these examples.
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More From: Journal of Physics A: Mathematical and Theoretical
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