nLab
factorization algebra of observables

Context

Higher algebra

Quantum field theory

Contents

Idea

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.

Examples

duality between algebra and geometry in physics:

algebrageometry
Poisson algebraPoisson manifold
deformation quantizationgeometric quantization
algebra of observablesspace of states
Heisenberg pictureSchrödinger picture
AQFTFQFT
higher algebrahigher geometry
Poisson n-algebran-plectic manifold
En-algebrashigher symplectic geometry
BD-BV quantizationhigher geometric quantization
factorization algebra of observablesextended quantum field theory
factorization homologycobordism representation

References

A fairly comprehensive account of factorization algebras as a formalization of perturbative quantum field theory (see at factorization algebra of observables) is in

and the beginning of

Lecture notes include

Last revised on December 21, 2016 at 05:14:07. See the history of this page for a list of all contributions to it.