Related papers: Quantum Monads in Phase Space and Related Toeplitz Operators

Quantum Monads in Phase Space and Related Toeplitz Operators

URL: http://arxiv.org/abs/2511.06491v1
Date: Sun, 09 Nov 2025 18:32:18 GMT
Title: Quantum Monads in Phase Space and Related Toeplitz Operators
Authors: Maurice de Gosson,
Abstract summary: In earlier work, we introduced quantum blobs as minimum-uncertainty symplectic ellipsoids in phase space.<n>These objects may be viewed as geometric monads in the Leibnizian sense.<n>We establish a one-to-one correspondence between such monads and generalized coherent states.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
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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