TY - CHAP

T1 - Algebraic Quantum Field Theory

AU - Halvorson, Hans

N1 - Funding Information: HH wishes to thank: Michael Müger for teaching him about the Doplicher-Roberts Theorem; the editors for their helpful feedback and patience; and David Baker, Tracy Lupher, and David Malament for corrections. MM gratefully acknowledges financial support by NWO via the Pioneer grant no.616.062.384 of N. P. Landsman and thanks Julien Bichon for a critical reading of the appendix and useful comments.

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84882876758&partnerID=8YFLogxK

U2 - 10.1016/B978-044451560-5/50011-7

DO - 10.1016/B978-044451560-5/50011-7

M3 - Book chapter

AN - SCOPUS:84882876758

SN - 9780444515605

SP - 731

EP - 864

BT - Philosophy of Physics

PB - Elsevier

ER -