Groupoid and algebra of the infinite quantum spin chain

DOI10.1016/j.geomphys.2023.104901zbMath1530.81095arXiv2302.01050MaRDI QIDQ6115707

Fabio Di Cosmo, Alberto Ibort, Unnamed Author, Florio M. Ciaglia, Giuseppe Marmo, Paolo Facchi

Publication date: 10 August 2023

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2302.01050

zbMATH Keywords

groupoidsHilbert algebrasinfinite spin chainSchwinger picture

Mathematics Subject Classification ID

Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Groups and algebras in quantum theory and relations with integrable systems (81R12) Operator algebra methods applied to problems in quantum theory (81R15) Hilbert algebras (46K15) Groupoids, semigroupoids, semigroups, groups (viewed as categories) (18B40)

Related Items (1)

The groupoidal picture of quantum mechanics

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On A. Connes' noncommutative integration theory
• The role of type III factors in quantum field theory
• On the modular structure of local algebras of observables
• On ergodic flows and the isomorphism of factors
• Theory of operator algebras. II
• Theory of operator algebras. III
• The local index formula in noncommutative geometry
• The emergence of time
• Projective limits of probability spaces
• Two soluble models of an antiferromagnetic chain
• Type I \(C^ *\)-algebras
• On the equilibrium states in quantum statistical mechanics
• Tomita's theory of modular Hilbert algebras and its applications
• Operator algebras. Theory of \(C^*\)-algebras and von Neumann algebras
• On rings of operators. III
• On rings of operators. IV
• QUANTUM MECHANICS AS QUANTUM MEASURE THEORY
• Decoherence, einselection, and the quantum origins of the classical
• Theory of Many-Particle Systems. I
• An amenable equivalence relation is generated by a single transformation
• Haar Measure for Measure Groupoids
• The Regular Representations of Measure Groupoids
• A gentle introduction to Schwinger’s formulation of quantum mechanics: The groupoid picture
• Von Neumann algebra automorphisms and time-thermodynamics relation in generally covariant quantum theories
• A quantum route to the classical Lagrangian formalism
• Quantum tomography and Schwinger’s picture of quantum mechanics*
• Feynman’s propagator in Schwinger’s picture of Quantum Mechanics
• Lagrangian description of Heisenberg and Landau–von Neumann equations of motion
• Une classification des facteurs de type ${\rm III}$
• Schwinger’s picture of quantum mechanics I: Groupoids
• On the von neumann algebras generated by field operators
• Type of von Neumann Algebra Associated with Free Field
• Global Structure in Von Neumann Algebras
• Representations of uniformly hyperfinite algebras and their associated von Neumannn rings
• A classification of factors
• Irreducible representations of operator algebras
• Theory of operator algebras I.

This page was built for publication: Groupoid and algebra of the infinite quantum spin chain