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• W4361802364 abstract "The purpose of this paper is to introduce statistical states through signals used as the probes of physical systems. Phase space is the arena of both quantum and classical mechanics. This work reviews the origin of information in signal theory as a gateway to understanding quantum information theory. Concepts of operational physics and Lie group representation theory are applied to the study of phase space measurements. A statistical model of Hamiltonian dynamics in the Koopman representation is a Hilbert bundle over a symplectic manifold. Bochner’s theorem and its relationship with group characters pave the way to statistical observables in classical physics through an extension of the Fourier transform. The natural extension to non-commutative signal theory gives rise to representations of dynamical groups like in quantum mechanics. Two methods of quantization are discussed with emphasis on the appearance of statistical states: Souriau’s functions of positive type and the more general scheme of star product quantization. Quantum Signals are described by states arising from representations of the SU(2) group on the Poincare sphere that are introduced in the deformation theory approach by the star exponential." @default.
• W4361802364 created "2023-04-05" @default.
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• W4361802364 date "2023-01-01" @default.
• W4361802364 modified "2023-09-27" @default.
• W4361802364 title "Phase Space Quantization II: Statistical Ideas" @default.
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• W4361802364 doi "https://doi.org/10.1007/978-981-19-9530-9_4" @default.
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