symmetric monoidal (∞,1)-category of spectra
functorial quantum field theory
Reshetikhin?Turaev model? / Chern-Simons theory
FQFT and cohomology
Given a local action functional on fields which are sections of a suitable field bundle, perturbation theory and renormalization allow to assign to open subsets of spacetime/worldvolume the corresponding quantum BV-complexes/Beilinson-Drinfeld algebras. This assignment is canonically equipped with the structure of a factorization algebra, the factorization algebra of observables of the theory.
This formalization of algebraic quantum field theory is similar to, but a bit different from, the notion of local net of observables.
Over a Riemann surface: vertex operator algebra (Gwilliam, section 6.3, section 6.5)
(…)
duality between algebra and geometry in physics:
A fairly comprehensive account of factorization algebras as a formalization of perturbative quantum field theory (see at factorization algebra of observables) is in
Kevin Costello, Owen Gwilliam, Factorization algebras in perturbative quantum field theory
Owen Gwilliam, Factorization algebras and free field theories PhD thesis (pdf)
and the beginning of
Lecture notes include
Kevin Costello (with Owen Gwilliam), Factorizaton algebras in perturbative quantum field theory in Strings, Field, Topology, Oberwolfach report No 28, 2009 (pdf)
This can also be found mentioned in the talk notes of the Northwestern TFT Conference 2009, see in particular
notes by Christoph Wockel, Talk by Kevin Costello
notes by Evan Jenkins on the same talk: Factorization algebras in perturbative quantum gravity
Last revised on December 21, 2016 at 05:14:07. See the history of this page for a list of all contributions to it.