Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bloch waves and Non-commutative Tori of Magnetic Translations   We review the Landau problem of an electron in a constant uniform magnetic
field. The magnetic translations are the invariant transformations of the free
Hamiltonian. A K\"ahler polarization of the plane has been used for the
geometric quantization. Under the assumption of quasi-periodicity of the
wavefunction the magnetic translations in the Bravais lattice generate a
non-commutative quantum torus. We concentrate on the case when the magnetic
flux density is a rational number. The Bloch wavefunctions form a
finite-dimensional module of the noncommutative torus of magnetic translations
as well as of its commutant which is the non-commutative torus of magnetic
translation in the dual Bravais lattice. The bi-module structure of the Bloch
waves is shown to be the connecting link between two Morita equivalent
non-commutative tori.

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The categories of this paper are: mtrl-th
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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: hep-th
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The categories of this paper are: ao-sci
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The categories of this paper are: physics
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con