Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quaternionic Madelung Transformation and Non-Abelian Fluid Dynamics   In the 1920's, Madelung noticed that if the complex Schroedinger wavefunction
is expressed in polar form, then its modulus squared and the gradient of its
phase may be interpreted as the hydrodynamic density and velocity,
respectively, of a compressible fluid. In this paper, we generalize Madelung's
transformation to the quaternionic Schroedinger equation. The non-abelian
nature of the full SU(2) gauge group of this equation leads to a richer, more
intricate set of fluid equations than those arising from complex quantum
mechanics. We begin by describing the quaternionic version of Madelung's
transformation, and identifying its ``hydrodynamic'' variables. In order to
find Hamiltonian equations of motion for these, we first develop the canonical
Poisson bracket and Hamiltonian for the quaternionic Schroedinger equation, and
then apply Madelung's transformation to derive non-canonical Poisson brackets
yielding the desired equations of motion. These are a particularly natural set
of equations for a non-abelian fluid, and differ from those obtained by
Bistrovic et al. only by a global gauge transformation. Because we have
obtained these equations by a transformation of the quaternionic Schroedinger
equation, and because many techniques for simulating complex quantum mechanics
generalize straightforwardly to the quaternionic case, our observation leads to
simple algorithms for the computer simulation of non-abelian fluids.

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The categories of this paper are: math
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph