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Groupoid and algebra of the infinite quantum spin chain

Authors :
Ciaglia, Florio Maria
Di Cosmo, Fabio
Facchi, Paolo
Ibort, Alberto
Konderak, Arturo
Marmo, Giuseppe
Source :
Journal of Geometry and Physics, Volume 191, 2023
Publication Year :
2023

Abstract

It is well known that certain features of a quantum theory cannot be described in the standard picture on a Hilbert space. In particular, this happens when we try to formally frame a quantum field theory, or a thermodynamic system with finite density. This forces us to introduce different types of algebras, more general than the ones we usually encounter in a standard course of quantum mechanics. We show how these algebras naturally arise in the Schwinger description of the quantum mechanics of an infinite spin chain. In particular, we use the machinery of Dirac-Feynman-Schwinger (DFS) states developed in recent works to introduce a dynamics based on the modular theory by Tomita-Takesaki, and consequently we apply this approach to describe the Ising model.<br />Comment: 42 pages, 1 figure

Subjects

Subjects :
Quantum Physics

Details

Database :
arXiv
Journal :
Journal of Geometry and Physics, Volume 191, 2023
Publication Type :
Report
Accession number :
edsarx.2302.01050
Document Type :
Working Paper
Full Text :
https://doi.org/10.1016/j.geomphys.2023.104901