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Fuzzy Riemann surfaces

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Arnlind,  Joakim
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Shimada,  Hidehiko
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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jhep062009047.pdf
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Citation

Arnlind, J., Bordemann, M., Hofer, L., Hoppe, J., & Shimada, H. (2009). Fuzzy Riemann surfaces. Journal of High Energy Physics, 2009(6): 047. doi:10.1088/1126-6708/2009/06/047.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-4625-D
Abstract
We introduce C-Algebras (quantum analogues of compact Riemann surfaces), defined by polynomial relations in non-commutative variables and containing a real parameter that, when taken to zero, provides a classical non-linear, Poisson-bracket, obtainable from a single polynomial C(onstraint) function. For a continuous class of quartic constraints, we explicitly work out finite dimensional representations of the corresponding C-Algebras.