Notions of infinity in quantum physics

In this article we will review some notions of infiniteness that appear in Hilbert space operators and operator algebras. These include proper infiniteness, Murray von Neumann’s classification into type I and type III factors and the class of Følner C*-algebras that capture some aspects of amenabili...

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Detalhes bibliográficos
Autores: Lledó, Fernando, Martínez, Diego
Formato: otro
Estado:Versión aceptada para publicación
Fecha de publicación:2019
País:España
Recursos:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/197120
Acesso em linha:http://hdl.handle.net/10261/197120
Access Level:acceso abierto
Palavra-chave:Amenability
Proper infiniteness
Quantum Physics
CAR-algebra
Descrição
Resumo:In this article we will review some notions of infiniteness that appear in Hilbert space operators and operator algebras. These include proper infiniteness, Murray von Neumann’s classification into type I and type III factors and the class of Følner C*-algebras that capture some aspects of amenability. We will also mention how these notions reappear in the description of certain mathematical aspects of quantum mechanics, quantum field theory and the theory of superselection sectors. We also show that the algebra of the canonical anti-commutation relations (CAR-algebra) is in the class of Følner C*-algebras.