We construct and characterize canonical purifications for general algebraic states, extending prior constructions by Woronowicz and by Dutta/Faulkner to general quantum theories. Given a state on a $*$ -algebra, the canonical purification is a state on a "doubled" algebra that admits an interpretation in terms of CRT reflection. This interpretation holds for all quantum theories, even in the absence of gravity. We then identify conditions under which canonical purifications are "pure" in the technical sense, compute their modular conjugations, and relate them to GNS and natural-cone purifications in certain settings. In an appendix, we develop a general theory of von Neumann algebras generated by unbounded $*$ -algebras. In a forthcoming paper with Caminiti and Capeccia, we provide an application of this general theory to the problem of excitability in quantum field theory.We construct and characterize canonical purifications for general algebraic states, extending prior constructions by Woronowicz and by Dutta/Faulkner to general quantum theories. Given a state on a $*$-algebra, the canonical purification is a state on a "doubled" algebra that admits an interpretation in terms of CRT reflection. This interpretation holds for all quantum theories, even in the absence of gravity. We then identify conditions under which canonical purifications are "pure" in the technical sense, compute their modular conjugations, and relate them to GNS and natural-cone purifications in certain settings. In an appendix, we develop a general theory of von Neumann algebras generated by unbounded $*$-algebras. In a forthcoming paper with Caminiti and Capeccia, we provide an application of this general theory to the problem of excitability in quantum field theory.

hep-thCross-listedarXiv:2512.17014Dec 22, 2025

Phase-space behavior of physical nonlinear coherent states

Mustapha Ziane, Abdessamad Belfakir, Erik Díaz-Bautista +2 more

Abstract In this paper, we construct the generalized su(1, 1) nonlinear coherent states for particular physical systems. We study the behavior of the Wigner function for coherent states built from differential operators that satisfy either a generalized Heisenberg algebra or a generalized su(1, 1) nonlinear algebra. The systems studied are the harmonic oscillator and those ones associated with Pöschl-Teller potentials. The results show that the Wigner function for the associated nonlinear coherent states is positive for small values of their convergence radius. Furthermore, the Wigner function for these coherent states depends on the corresponding algebraic structure.Abstract In this paper, we construct the generalized su(1, 1) nonlinear coherent states for particular physical systems. We study the behavior of the Wigner function for coherent states built from differential operators that satisfy either a generalized Heisenberg algebra or a generalized su(1, 1) nonlinear algebra. The systems studied are the harmonic oscillator and those ones associated with Pöschl-Teller potentials. The results show that the Wigner function for the associated nonlinear coherent states is positive for small values of their convergence radius. Furthermore, the Wigner function for these coherent states depends on the corresponding algebraic structure.

Physica ScriptaOct 22, 20200 citations

Generalized coherent states for arbitrary quantum systems

Jean‐Pierre Gazeau, Pascal Monceau

Springer eBooksJan 1, 200020 citations

Generalized Grassmann variables for quantum kit (k-level) systems and Barut–Girardello coherent states for su(r + 1) algebras

Mohammed Daoud A, L. Gouba

This paper concerns the construction of su(r + 1) Barut–Girardello coherent states in terms of generalized Grassmann variables. We first introduce a generalized Weyl–Heisenberg algebra A(r) (r≥1) generated by r pairs of creation and annihilation operators. This algebra provides a useful framework to describe qubit and qukit (k-level) systems. It includes the usual Weyl–Heisenberg and su(2) algebras. We investigate the corresponding Fock representation space. The generalized Grassmann variables are introduced as variables spanning the Fock-Bargmann space associated with the algebra A(r). The Barut–Girardello coherent states for su(r + 1) algebras are explicitly derived and their over-completion properties are discussed.This paper concerns the construction of su(r + 1) Barut–Girardello coherent states in terms of generalized Grassmann variables. We first introduce a generalized Weyl–Heisenberg algebra A(r) (r≥1) generated by r pairs of creation and annihilation operators. This algebra provides a useful framework to describe qubit and qukit (k-level) systems. It includes the usual Weyl–Heisenberg and su(2) algebras. We investigate the corresponding Fock representation space. The generalized Grassmann variables are introduced as variables spanning the Fock-Bargmann space associated with the algebra A(r). The Barut–Girardello coherent states for su(r + 1) algebras are explicitly derived and their over-completion properties are discussed.

arXiv:1703.00833Journal of Mathematical PhysicsMay 1, 20172 citations

We construct and characterize canonical purifications for general algebraic states, extending prior constructions by Woronowicz and by Dutta/Faulkner to general quantum theories. Given a state on a

*

-algebra, the canonical purification is a state on a "doubled" algebra that admits an interpretation in terms of CRT reflection. This interpretation holds for all quantum theories, even in the absence of gravity. We then identify conditions under which canonical purifications are "pure" in the technical sense, compute their modular conjugations, and relate them to GNS and natural-cone purifications in certain settings. In an appendix, we develop a general theory of von Neumann algebras generated by unbounded

*

-algebras. In a forthcoming paper with Caminiti and Capeccia, we provide an application of this general theory to the problem of excitability in quantum field theory.