Algebraic Quantum Field Theory

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Abstract

This chapter discusses the algebraic quantum field theory (AQFT). The chapter describes the theorem with suitable examples. It discusses the relations between microcausality and other independence assumptions for the algebras A(O1),A(O2). Some results concerning violation of Bell's inequality in AQFT are summarized. A generalized notion of Bell type measurements for a pair of von Neumann algebras is also discussed in the chapter. Quantum field theory is devoted to assessing the status of particles from the point of view of AQFT. The "modal" interpretation of quantum mechanics is similar to the de Broglie-Bohm theory, but begins from a more abstract perspective on the question of assigning definite values to some observables. Roberts' shows how Bose-Fermi particle statistics emerges naturally from the Doplicher, Haag, and Roberts (DHR) analysis of physical representations of the algebra of observables. Roberts' claim is of relevance to the philosophical debate about statistics and identical particles. The philosophers have inquired, "what explains Bose-Fermi statistics?" Roberts' answer has been that the explanation comes from the structure of the category of representations of the observable algebra.

Original languageEnglish (US)
Title of host publicationPhilosophy of Physics
PublisherElsevier
Pages731-864
Number of pages134
ISBN (Print)9780444515605
DOIs
StatePublished - 2007

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy

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