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arXiv · 2511.06491

Quantum Monads in Phase Space and Related Toeplitz Operators

Maurice de Gosson
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Abstract

In earlier work, we introduced quantum blobs as minimum-uncertainty symplectic ellipsoids in phase space. These objects may be viewed as geometric monads in the Leibnizian sense, representing the elementary units of phase-space structure consistent with the uncertainty principle. We establish a one-to-one correspondence between such monads and generalized coherent states, represented by arbitrary non-degenerate Gaussian wave functions in configuration space. To each of these states, we associate a classs of Toeplitz operators that extends the standard anti-Wick quantization scheme. The mathematical and physical properties of these operators are analyzed, allowing for a generalized definition of density matrices within the phase-space formulation of quantum mechanics.

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Maurice de Gosson. 2025-11-09. Quantum Monads in Phase Space and Related Toeplitz Operators. https://arxiv.org/abs/2511.06491

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