Von Neumann algebras associated to quantum-mechanical constants of motion

DOI10.1007/BF01205484zbMath0633.46066MaRDI QIDQ1096147

Alexander Grossmann, Joseph Slawny

Publication date: 1986

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

Weyl operatorconstants of motionmultiplierbi-characterinvariance of the classical Hamiltonian under a group of translations in phase spacevon Neumann algebras generated by restrictions of the Weyl system to arbitrary closed subgroups

Mathematics Subject Classification ID

Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Applications of selfadjoint operator algebras to physics (46L60) Geometry and quantization, symplectic methods (81S10) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Miscellaneous applications of functional analysis (46N99)

Cites Work

• Classification of injective factors. Cases \(\mathrm{II}_1\), \(\mathrm{II}_\infty\), \(\mathrm{III}_\lambda\), \(\lambda\neq 1\)
• Die Eindeutigkeit der Schrödingerschen Operatoren
• The \(C^ *\)-algebras of a free Boson field
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