AQFT and operator algebra

Definitions

• quantum mechanical system

  • observable

    • operator algebra

      • C*-algebra

      • von Neumann algebra

    • subsystem

  • state,

    • cyclic vector, separating vector

• local net of observables

  • Haag-Kastler axioms

  • Wightman axioms

  • causal net

  • field net

  • conformal net

Theorems

States and observables

• Kochen-Specker theorem

• Gleason's theorem

• Wigner theorem

Operator algebra

• GNS construction

• modular theory

• Fell's theorem

• Stone-von Neumann theorem

• Haag's theorem

Local QFT

• Reeh-Schlieder theorem

• Bisognano-Wichmann theorem

• PCT theorem

• spin-statistics theorem

• DHR superselection theory

Euclidean QFT

• Osterwalder-Schrader theorem