• Corpus ID: 233864887

Berezin-Toeplitz Quantization in Real Polarizations with Toric Singularities

@inproceedings{Leung2021BerezinToeplitzQI,
  title={Berezin-Toeplitz Quantization in Real Polarizations with Toric Singularities},
  author={Naichung Conan Leung and Yutung Yau},
  year={2021}
}
On a compact Kähler manifold X, Toeplitz operators determine a deformation quantization (C∞(X,C)[[~]], ⋆) with separation of variables [10] with respect to transversal complex polarizations T X, T X as ~ → 0 [15]. The analogous statement is proved for compact symplectic manifolds with transversal non-singular real polarizations [13]. In this paper, we establish the analogous result for transversal singular real polarizations on compact toric symplectic manifolds X. Due to toric singularities… 

References

SHOWING 1-10 OF 16 REFERENCES
Degeneration of Kähler structures and half-form quantization of toric varieties
We study the half-form Kahler quantization of a smooth symplectic toric manifold (X,ω), such that [ω/2π]− c1(X)/2 ∈ H(X,Z) and is nonnegative. We define the half-form corrected quantization of (X,ω)
Deformation quantization via Toeplitz operators on geometric quantization in real polarizations
In this paper, we study quantization on a compact integral symplectic manifold X with transversal real polarizations. In the case of complex polarizations, namely X is Kähler equipped with
Deformation quantization using groupoids. The case of toric manifolds
Deformation quantizations with separation of variables on a Kähler manifold
We give a simple geometric description of all formal differentiable deformation quantizations on a Kähler manifoldM such that for each open subsetU⊂M ⋆-multiplication from the left by a holomorphic
Magnitude of fourier coefficients and degree of approximation by riemann sums
We compare rates of decay of the cosine Fourier coefficients of a 2φ-periodic function f with that of Riemann sum of f over [0, 2φ] minus .
The geometry of a bi-Lagrangian manifold
Toeplitz quantization of Kähler manifolds anggl(N), N→∞ limits
For general compact Kähler manifolds it is shown that both Toeplitz quantization and geometric quantization lead to a well-defined (by operator norm estimates) classical limit. This generalizes
Identification of Berezin-Toeplitz Deformation Quantization
We give a complete identification of the deformation quantization which was obtained from the Berezin- Toeplitz quantization on an arbitrary compact Kahler manifold. The deformation quantization with
Locality in GNS Representations of Deformation Quantization
Abstract: In the framework of deformation quantization we apply the formal GNS construction to find representations of the deformed algebras in pre-Hilbert spaces over ℂ[[λ]] and establish the notion
Deformation quantization of compact Kahler manifolds by Berezin-Toeplitz quantization
For arbitrary compact quantizable Kahler manifolds it is shown how a natural formal deformation quantization (star product) can be obtained via Berezin-Toeplitz operators. Results on their
...
...