Abstract
The fuzzy disc, introduced by the authors of [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 the fuzzy disc in terms of operators and their commutation relations, and studied properties of angular projection operators. A similar construction for the fuzzy annulus is also given. As an application, we constructed fan-shaped soliton solutions of a scalar field theory on the fuzzy disc. We also applied this concept to the theory of noncommutative gravity we proposed in [2]. In addition, possible connections to some systems in physics are suggested.
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