ALGEBRAS OF UNBOUNDED OPERATORS AND PHYSICAL APPLICATIONS: A SURVEY

DOI10.1142/S0129055X07002961zbMath1144.82301arXiv0903.5446OpenAlexW2963521267MaRDI QIDQ3444899

Fabio Bagarello

Publication date: 5 June 2007

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

Full work available at URL: https://arxiv.org/abs/0903.5446

zbMATH Keywords

algebraic dynamicsalgebras of unbounded operatorsquantum systems with infinite degrees of freedom

Mathematics Subject Classification ID

Algebras of unbounded operators; partial algebras of operators (47L60) General theory of (C^*)-algebras (46L05) Quantum equilibrium statistical mechanics (general) (82B10) Quantum dynamics and nonequilibrium statistical mechanics (general) (82C10)

Related Items (19)

Coordinate representation for non-Hermitian position and momentum operators ⋮ Uncertainty relation for non-Hermitian operators ⋮ Gibbs states, algebraic dynamics and generalized Riesz systems ⋮ Extended SUSY quantum mechanics, intertwining operators and coherent states ⋮ Structure of locally convex quasi \(C^*\)-algebras ⋮ A description of pseudo-bosons in terms of nilpotent Lie algebras ⋮ Locally convex quasi \(C^{*}\)-normed algebras ⋮ Integrable representations of involutive algebras and Ore localization ⋮ Pseudo-bosons for the \(D_2\) type quantum Calogero model ⋮ On quantum statistical mechanics: a study guide ⋮ Transition probabilities for non self-adjoint Hamiltonians in infinite dimensional Hilbert spaces ⋮ Some results on the dynamics and transition probabilities for non self-adjoint Hamiltonians ⋮ Unbounded representations of \(q\)-deformation of Cuntz algebra ⋮ Representations and derivations of quasi \(*\)-algebras induced by local modifications of states ⋮ O ⋆ -algebras and quantum dynamics: Some existence results ⋮ Representable states on quasilocal quasi *-algebras ⋮ Crossed products of algebras of unbounded operators ⋮ Coupled Susy, pseudo-bosons and a deformed su(1,1) Lie algebra ⋮ Abstract ladder operators and their applications

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Partial *-algebras of closed linear operators in Hilbert space
• Local algebras of observables and pointlike localized fields
• Dynamics of mean-field spin models from basic results in abstract differential equations
• ``Almost mean-field Ising model: An algebraic approach
• Fixed points in topological *-algebras of unbounded operators.
• \(L^p\)-spaces as quasi \(^*\)-algebras
• On the mathematical structure of the B.C.S.-model
• On the equilibrium states in quantum statistical mechanics
• Some classes of topological quasi $*$-algebras
• Mathematical structures for long-range dynamics and symmetry breaking
• Canonical commutation relations on the interval
• New structures in the theory of the laser model. II. Microscopic dynamics and a nonequilibrium entropy principle
• Algebraic dynamics in O*-algebras: A perturbative approach
• New methods and structures in the theory of the multi-mode Dicke laser model
• The Heisenberg dynamics of spin systems: A quasi*-algebras approach
• Bounded elements and spectrum in Banach quasi^*-algebras
• Quasi *-algebras of measurable operators
• An Algebraic Approach to Quantum Field Theory
• Time Translations in the Algebraic Formulation of Statistical Mechanics
• Morphisms of certain Banach \(C^*\)-modules

This page was built for publication: ALGEBRAS OF UNBOUNDED OPERATORS AND PHYSICAL APPLICATIONS: A SURVEY