(no subject)

[leblon]

OK, I think I finally figured out how to show that the algebra of local observables in a free field theory is a von Neumann algebra of Type III. Or at least, why it is not Type I. Everything boils down to checking that a certain integral operator on the space of functions in a bounded region is not trace-class, which in turn is due to short-distance singularities in the correlators of fields across the boundary. As a by product, I learned some representation theory for canonical commutation relations (CCR) due to Araki.

Comments

[vladimir-anski.livejournal.com]

Интересно было бы посмотреть. А, кстати, не поймите меня правильно, но разве бывают наблюдаемые в свободной теории? Разве свободную теорию не пишут для принципиально ненаблюдаемых голых частиц?