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Non-commutative ADE geometries as holomorphic wave equations

Adil Belhaj·Jorgen Rasmussen·El Hassan Saidi·Abdellah Sebbar
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Abstract

Borrowing ideas from the relation between classical and quantum mechanics, we study a non-commutative elevation of the ADE geometries involved in building Calabi-Yau manifolds. We derive the corresponding geometric hamiltonians and the holomorphic wave equations representing these non-commutative geometries. The spectrum of the holomorphic waves is interpreted as the quantum moduli space. Quantum A_1 geometry is analyzed in some details and is found to be linked to the Whittaker differential equation.

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Adil Belhaj, Jorgen Rasmussen, El Hassan Saidi, Abdellah Sebbar. 2005-09-09. Non-commutative ADE geometries as holomorphic wave equations. https://doi.org/10.1016/j.nuclphysb.2005.08.039

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