On quasi-equivalence of quasifree states of the canonical commutation relations

DOI10.2977/prims/1195183576zbMath0505.46052OpenAlexW2000418123MaRDI QIDQ1836082

Shigeru Yamagami, Huzihiro Araki

Publication date: 1982

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1195183576

zbMATH Keywords

canonical commutation relationsgauge-invariantHilbert Schmidt classquasi- equivalent representationsquasifree states of CCR

Mathematics Subject Classification ID

Axiomatic quantum field theory; operator algebras (81T05) Applications of selfadjoint operator algebras to physics (46L60) Commutation relations and statistics as related to quantum mechanics (general) (81S05) States of selfadjoint operator algebras (46L30)

Related Items

Modular structure of the Weyl algebra ⋮ Local normality of infravacua and relative normalizers for relativistic systems ⋮ GEOMETRY OF COHERENT STATES OF CCR ALGEBRAS ⋮ Hafnian point processes and quasi-free states on the CCR algebra ⋮ Local nets of von Neumann algebras in the sine-Gordon model ⋮ Kakutani dichotomy on free states ⋮ Modular nuclearity: a generally covariant perspective ⋮ Remarks on BEC on graphs ⋮ Scaling limits of lattice quantum fields by wavelets ⋮ Quantum fields in curved spacetime ⋮ GEOMETRY OF QUASI-FREE STATES OF CCR ALGEBRAS ⋮ Scaling flow on covariance forms of CCR algebras ⋮ Local quasiequivalence and adiabatic vacuum states ⋮ Local definiteness, primarity and quasiequivalence of quasifree Hadamard quantum states in curved spacetime

Cites Work

• Analytic vectors
• An inequality for Hilbert-Schmidt norm
• Functional calculus for sesquilinear forms and the purification map
• Some properties of modular conjugation operator of von Neumann algebras and a non-commutative Radon-Nikodym theorem with a chain rule
• Quasi-equivalence of quasi-free states on the Weyl algebra
• On quasifree states of the canonical commutation relations. I
• On quasifree states of the canonical commutation relations. II
• Distributions in Hilbert Space and Canonical Systems of Operators
• Linear Symmetries of Free Boson Fields