The role of type III factors in quantum field theory

Autor(en)

Jakob Yngvason

Abstrakt

One of von Neumann's motivations for developing the theory of operator algebras and his and Murray's 1936 classification of factors was the question of possible decompositions of quantum systems into independent parts. For quantum systems with a finite number of degrees of freedom the simplest possibility, i.e. factors of type I in the terminology of Murray and von Neumann, are perfectly adequate. In relativistic quantum field theory (RQFT), on the other hand, factors of type III occur naturally. The same holds true in quantum statistical mechanics of infinite systems. In this brief review some physical consequences of the type III property of the von Neumann algebras corresponding to localized observables in RQFT and their difference from the type I case will be discussed. The cumulative effort of many people over more than 30 years has established a remarkable uniqueness result: The local algebras in RQFT are generically isomorphic to the unique, hyperfinite type III, factor in Connes' classification of 1973. Specific theories are characterized by the net structure of the collection of these isomorphic algebras for different space-time regions, i.e. the way they are embedded into each other.

Organisation(en)

Mathematische Physik

Externe Organisation(en)

Erwin Schrödinger Institut

Journal

Reports on Mathematical Physics

Band

55

Seiten

135-147

Anzahl der Seiten

13

ISSN

0034-4877

DOI

https://doi.org/10.1016/S0034-4877(05)80009-6

Publikationsdatum

2005

Peer-reviewed

Ja

ÖFOS 2012

103036 Theoretische Physik

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/1f1b6fe5-66e4-4007-b8ad-b96b8c48620d