2012/06/30 by Shinpei Kobayashi, Tsuguhiko Asakawa
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #Orbital Angular Momentum in Optics #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.1007/jhep04(2013)145
published as JHEP 1304:145,2013 · 24 pages, 12 figures; v2: minor mistake corrected in Eq.(3.21), and discussion adapted accordingly; v3: a further discussion on the algebra of the fuzzy disc added in subsection 3.2; v4: discussions improved and typos corrected
openalex publication_date 2013/04/01 · arxiv created 2013/05/20 · arxiv updated 2013/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.