The Heisenberg dynamics of spin systems: A quasi*-algebras approach

DOI10.1063/1.531652zbMath0896.46048OpenAlexW1992589080MaRDI QIDQ5284856

Fabio Bagarello, Camillo Trapani

Publication date: 5 October 1998

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

Full work available at URL: https://doi.org/10.1063/1.531652

zbMATH Keywords

\(CQ^*\)-algebrasspin systemsalgebraic dynamicsmean-field modelsthermodynamical limitbubble modelsquasilocal \(C^*\)-algebraquasi\(^*\)-algebras

Mathematics Subject Classification ID

Model quantum field theories (81T10) Applications of selfadjoint operator algebras to physics (46L60) Applications of functional analysis in quantum physics (46N50)

Related Items (15)

TOPOLOGICAL PARTIAL *-ALGEBRAS: BASIC PROPERTIES AND EXAMPLES ⋮ Empirical underdetermination for physical theories in \(C^*\) algebraic setting: comments to an Arageorgis's argument ⋮ ALGEBRAS OF UNBOUNDED OPERATORS AND PHYSICAL APPLICATIONS: A SURVEY ⋮ Representable and continuous functionals on Banach quasi \(*\)-algebras ⋮ Some classes of topological quasi $*$-algebras ⋮ On some applications of representable and continuous functionals of Banach quasi \(^\ast \)-algebras ⋮ Applications of Generalized B∗-Algebras to Quantum Mechanics ⋮ Homomorphisms and derivations in proper \(JCQ^{*}\)-triples ⋮ Locally convex quasi \(C^{*}\)-normed algebras ⋮ Applications of topological*-algebras of unbounded operators ⋮ Representations and derivations of quasi \(*\)-algebras induced by local modifications of states ⋮ Tensor products of normed and Banach quasi \(^*\)-algebras ⋮ Unbounded derivations and \(^*\)-automorphisms groups of Banach quasi \(^*\)-algebras ⋮ O ⋆ -algebras and quantum dynamics: Some existence results ⋮ Fixed points in topological *-algebras of unbounded operators.

Cites Work

• Partial \({}^*\)-algebras of closable operators. I: The basic theory and the abelian case
• Algebras of unbounded operators and quantum dynamics
• Partial *-algebras of closed linear operators in Hilbert space
• Partial \(\star\)-algebras of closable operators. II: States and representations of partial \(\star\)-algebras
• Dynamics of mean-field spin models from basic results in abstract differential equations
• ``Almost mean-field Ising model: An algebraic approach
• \(CQ^*\)-algebras: Structure properties
• On the mathematical structure of the B.C.S.-model
• States and derivations on quasi-*-algebras
• The dynamics of a class of quantum mean-field theories
• QUASI *-ALGEBRAS OF OPERATORS AND THEIR APPLICATIONS
• PARTIAL *-ALGEBRAS OF CLOSABLE OPERATORS: A REVIEW
• An Algebraic Approach to Quantum Field Theory

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