The beat of a fuzzy drum: fuzzy Bessel functions for the disc

Abstract

The fuzzy disc is a matrix approximation of the functions on a disc which preserves rotational symmetry. In this paper we introduce a basis for the algebra of functions on the fuzzy disc in terms of the eigenfunctions of a properly defined fuzzy Laplacian. In the commutative limit they tend to the eigenfunctions of the ordinary Laplacian on the disc, i.e. Bessel functions of the first kind, thus deserving the name of fuzzy Bessel functions.

arXiv comment30 pages, 8 figures

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Cited by in corpus (11)

• New Approach to Nonperturbative Quantum Mechanics with Minimal Length Uncertainty
• Numerical simulations of a non-commutative theory: the scalar model on the fuzzy sphere
• Noncommutative field theories on $R_{\lambda }^3$: Towards UV/IR mixing freedom
• Quantum gauge theories on noncommutative 3-d space
• Matrix Bases for Star Products: a Review
• Curing the UV/IR mixing for field theories with translation-invariant $\star$ products
• Boundaries in the Moyal plane
• Non-constant Non-commutativity in 2d Field Theories and a New Look at Fuzzy Monopoles
• Asymptotic commutativity of quantized spaces: the case of ${\mathbb{CP}}^{p,q}$
• Noncommutative Spherically Symmetric Spaces
• Noncommutative Q-Lumps