The Twistor Space of R4n and Berezin–Toeplitz Operators.

A hyperkähler manifold M has a family of induced complex structures indexed by a two-dimensional sphere S 2 ≅ CP 1 . The twistor space of M is a complex manifold Tw (M) together with a natural holomorphic projection Tw (M) → CP 1 , whose fiber over each point of CP 1 is a copy of M with the corresponding induced complex structure. We remove one point from this sphere (corresponding to one fiber in the twistor space), and for the case of M = R 4 n , n ∈ N , equipped with the standard hyperkähler structure, we construct one quantization that replaces the family of Berezin–Toeplitz quantizations parametrized by S 2 - { p t } . We provide semiclassical asymptotics for this quantization. [ABSTRACT FROM AUTHOR]