Optimal Remainder Estimates in the Quantization of Complex Projective Spaces

2025/08/27 by Aschieri, Tommaso, Ruba, Błażej, Solovej, Jan Philip
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2508.19968

Abstract

We study Berezin-Toeplitz quantization of complex projective spaces \mathbbCP^d-1 and obtain full asymptotic expansions of the Berezin transformation and of products of Toeplitz operators. In each case, the remainder is controlled by the next term of the expansion, either through a positivity-preserving transformation or via an operator inequality. This leads to bounds which are optimal in terms of the required regularity and feature sharp or asymptotically sharp constants.

Citations

• A Representation Theoretic Approach to Toeplitz Quantization on Flag Manifolds
• Asymptotics of unitary matrix elements in canonical bases
• SU(2)-equivariant quantum channels: semiclassical analysis
• Analytic Berezin-Toeplitz operators
• Toeplitz operators with analytic symbols
• Spectral aspects of the Berezin transform
• Sharp correspondence principle and quantum measurements
• Identification of Berezin-Toeplitz deformation quantization
• Deformation quantization of compact Kaehler manifolds by Berezin-Toeplitz quantization
• Deformation Quantization of Kahler Manifolds
• Geometric quantization and multiplicities of group representations
• Invariant Affine Connections on Homogeneous Spaces

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