Angles in fuzzy disc and angular noncommutative solitons

作者：Kobayashi Shinpei^*; Asakawa Tsuguhiko

来源：The Journal of High Energy Physics, 2013, 2013(4): 145.

DOI：10.1007/JHEP04(2013)145

• Non-Commutative Geometry
• Models of Quantum Gravity
• Tachyon Condensation
• D-branes

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.

• 出版日期2013-4