Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Berezin quantization and unitary representations of Lie groups   In 1974, Berezin proposed a quantum theory for dynamical systems having a
K\"{a}hler manifold as their phase space. The system states were represented by
holomorphic functions on the manifold. For any homogeneous K\"{a}hler manifold,
the Lie algebra of its group of motions may be represented either by
holomorphic differential operators (``quantum theory"), or by functions on the
manifold with Poisson brackets, generated by the K\"{a}hler structure
(``classical theory"). The K\"{a}hler potentials and the corresponding Lie
algebras are constructed now explicitly for all unitary representations of any
compact simple Lie group. The quantum dynamics can be represented in terms of a
phase-space path integral, and the action principle appears in the
semi-classical approximation.

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The categories of this paper are: cs
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The categories of this paper are: physics
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The categories of this paper are: cmp-lg
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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th