Seminar on Algebraic quantum field theory (WISM447)
Spring 2013. 7.5 ects.
This seminar meets twice a week, in room 610:     Wednesdays 10:00-12:00, and Fridays 13:00-15:00.
The Wednesday meetings will consist of talks given by the participants.
The Friday meetings will be there for informal discussions and/or a lecture by myself.

---

List of topics:
• Wightman axioms and Haag Kastler axioms (Bram) Notes
[Araki]: Section 4.8; [Haag]: begin of Chapter 2 and begin of chapter 3; [BFV]: seciton 2.2
• Free fields (Jules)
[Araki]: 3.5 and appendix; [BFV]: section 2.3; [BMT]
• Conformal field theory in 1+1 dimensions (Laurent) Notes
[BGL] without the stuff on the Misognano-Wichmann theorem; [LR-04] up to section 2.
• Conformal nets, first examples: current algebras (Peter) Notes
[GF], [BMT]
• Structure theory of conformal nets: Reeh-Shlieder theorem (Laura) Notes
[Longo] sections 6.2 and 3.2
• (2x) Structure theory of conformal nets: Bisognano-Wichmann theorem (Shan) Notes1  Notes2
[Longo] Chapter 2, Sections 6.2 and 3.2
• More examples of conformal nets: Virasoro and lattices (Joost N.) Notes
[Carpi] up to Section 2, [Dong-Xu], [Staszkiewicz]
• Superselection theory (=representations) (Laurent) Notes1  Notes2
[GF], [Mü] Section 2.2, [Haag] IV.2
• The Spin-statistics theorem (Bram) [GL] Exercise
• Q-systems (=Frobenius algebras) and extensions of conformal nets (Laura) Notes
[Pennig] Section 3; [LR-94]
• The Virasoro net and the classification of conformal nets with c<1 (Shan) Notes
[Pennig] Section 2; [KL-03]
• The equivalence bewteen chiral non-local and non-chiral local conformal nets (Joost N.)
[LR-04], [LR-08], [Rehren]
• The classification of full CFTs with c<1 (Peter)
[Pennig], [KL-03b], [KLRP]

---

References:
[Araki]: Mathematical theory of quantum fields. Amazon
[BFV] Brunetti, Fredenhagen, Verch: The generally covariant locality principle - A new paradigm for local quantum field theory. arXiv
[BGL] Brunetti, Guido, Longo: Modular structure and duality in conformal quantum field theory. arXiv
[BMT] Buchholz, Mack, Todorov: The current algebra on the circle as a germ of local field theories. Elsevier
[Carpi] On the representation theory of Virasoro nets. arXiv
[Dong-Xu] Conformal nets associated to lattices and their orbifolds. arXiv
[GF] Gabbiani, Frölich: Operator algebras and conformal field theory. Euclid
[GL] Guido, Longo: The conformal and spin statistics theorem. arXiv
[Haag]: Local quantum Physics: Fields, particles, algebras. Amazon
[KL-03]: Kawahigashi, Longo: Classification of Local Conformal Nets. Case c<1 arXiv
[KL-03b]: Kawahigashi, Longo: Classification of Two-dimensional Local Conformal Nets with c<1 and 2-cohomology Vanishing for Tensor Categories. arXiv
[KLRP]: Kawahigashi, Longo, Rehren, Pennig: The classification of non-local chiral CFT with c<1. arXiv
[Longo]: Roberto Longo: Lecture notes on Conformal nets I and II (available from his webpage).
[LR-94]: Longo, Rehren: Nets of subfactors arXiv
[LR-04]: Longo, Rehren: Local fields in boundary conformal QFT. arXiv
[LR-08]: Longo, Rehren: How to remove the boundary in CFT. arXiv
[Mü]: Michael Müger: On the structure and representation theory of rational chiral conformal theories. notes
[Pennig]: Sektorstruktur und Klassifikation von zwei dimensionalen, konformen Quantenfeldtheorien auf dem Halb raum. pdf
[Staszkiewicz]: Die lokale Struktur abelscher Stromalgebren auf dem Kreis. PhD thesis