Groupoid and algebra of the infinite quantum spin chain Articles uri icon

publication date

  • September 2023

start page

  • 1

end page

  • 23


  • 104901


  • 191

International Standard Serial Number (ISSN)

  • 0393-0440

Electronic International Standard Serial Number (EISSN)

  • 1879-1662


  • 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.


  • Mathematics
  • Physics


  • schwinger picture; algebras; groupoids; quantum fields theory; spin chain