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Boundaries in the Moyal plane. (English) Zbl 1342.81633
Summary: We study the oscillations of a scalar field on a noncommutative disc implementing the boundary as the limit case of an interaction with an appropriately chosen confining background. The space of quantum fluctuations of the field is finite dimensional and displays the rotational and parity symmetry of the disc. We perform a numerical evaluation of the (finite) Casimir energy and obtain similar results as for the fuzzy sphere and torus.
##### MSC:
 81T75 Noncommutative geometry methods in quantum field theory
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