Non-commutative image geometries as holomorphic wave equations Original Research Article

Borrowing ideas from the relation between classical and quantum mechanics, we study a non-commutative elevation of the image 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 image geometry is analyzed in some details and is found to be linked to the Whittaker differential equation.