Chong, C. C.; Vourdas, A. Quantum correlations and the extended phase space. (English) Zbl 0992.81043 J. Phys. A, Math. Gen. 34, No. 46, 9849-9860 (2001). Summary: An extended phase space \(x\)-\(p\)-\(X\)-\(P\) is introduced for one-mode systems, where \(x\)-\(p\) is the position-momentum plane and \(X\)-\(P\) is the quantum correlations plane. The Wigner functions \(W(x, p)\) and the Weyl functions \(\widetilde W(X,P)\) for arbitrary operators are studied in this space. Creation and annihilation operators for Wigner and Weyl functions are introduced and are used to perform displacements and squeezing in the \(x\)-\(p\)-\(X\)-\(P\) extended phase space. The formalism can be used for the construction of quantum states with desirable correlation properties. MSC: 81S30 Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics 81V80 Quantum optics Keywords:creation and annihilation operators; one-mode systems; Wigner functions; Weyl functions; displacements; squeezing PDFBibTeX XMLCite \textit{C. C. Chong} and \textit{A. Vourdas}, J. Phys. A, Math. Gen. 34, No. 46, 9849--9860 (2001; Zbl 0992.81043) Full Text: DOI