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arXiv · 1206.6602

Angles in Fuzzy Disc and Angular Noncommutative Solitons

Shinpei Kobayashi·Tsuguhiko Asakawa
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Abstract

The fuzzy disc, introduced by the authors of Ref.[1], is a disc-shaped region in a noncommutative plane, and is a fuzzy approximation of a commutative disc. In this paper we show that one can introduce a concept of angles to the fuzzy disc, by using the phase operator and phase states known in quantum optics. We gave a description of a fuzzy disc in terms of operators and their commutation relations, and studied properties of angular projection operators. A similar construction for a fuzzy annulus is also given. As an application, we constructed fan-shaped soliton solutions of a scalar field theory on a fuzzy disc, which corresponds to a fan-shaped D-brane. We also applied this concept to the theory of noncommutative gravity that we proposed in Ref.[2]. In addition, possible connections to black hole microstates, holography and an experimental test of noncommutativity by laser physics are suggested.

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Shinpei Kobayashi, Tsuguhiko Asakawa. 2013-05-20. Angles in Fuzzy Disc and Angular Noncommutative Solitons. https://doi.org/10.1007/jhep04(2013)145

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