Boundaries in the Moyal plane
H. Falomir, S.A. Franchino Vi\~nas, P.A.G. Pisani, F. Vega
TL;DR
This paper investigates scalar field oscillations on a noncommutative disc, analyzing boundary effects, quantum fluctuations, and Casimir energy, revealing symmetry properties and finite-dimensional fluctuation spaces.
Contribution
It introduces a novel approach to boundary conditions in the Moyal plane using a confining background, leading to finite quantum fluctuation spaces and numerical Casimir energy evaluation.
Findings
Quantum fluctuations form a finite-dimensional space with disc symmetries.
Casimir energy computed numerically shows similarities to fuzzy sphere and torus cases.
Boundary implementation affects fluctuation spectrum and energy calculations.
Abstract
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.
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