Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Harmonic Oscillator in the Plane and the Jordan-Schwinger Algebras   The direct and indirect Lagrangian representations of the planar harmonic
oscillator have been discussed. The reduction of these Lagrangians in their
basic forms characterising either chiral, or pseudo - chiral oscillators have
been given. A Hamiltonian analysis, showing its equivalence with the Lagrangian
formalism has also been provided. Finally, we show that the chiral and pseudo -
chiral modes act as dynamical structures behind the Jordan - Schwinger
realizations of the SU(2) and SU(1,1) algebras. Also, the SU(1,1) construction
found here is different from the standard Jordan - Schwinger form.

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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: math
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph