Berezin quantization is extended to holomorphic symplectic manifolds by using rank-n projections on cotangent bundles of Grassmannians, and this is shown equivalent to a holomorphic path integral quantization.
On an Axiomatization of Path Integral Quantization and its Equivalence to Berezin's Quantization
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We axiomatize path integral quantization of symplectic manifolds. We prove that this path integral formulation of quantization is equivalent to an abstract operator formulation, ie. abstract coherent state (or Berezin) quantization. We use the corresponding path integral of Poisson manifolds to quantize all complete Riemann surfaces of constant non$\unicode{x2013}$positive curvature and some Poisson structures on the sphere.
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Quantization of Holomorphic Symplectic Manifolds: Analytic Continuation of Path Integrals and Coherent States
Berezin quantization is extended to holomorphic symplectic manifolds by using rank-n projections on cotangent bundles of Grassmannians, and this is shown equivalent to a holomorphic path integral quantization.