Mathematical Quantum Field Theory

Axiomatization/Formalization#

There are two main approaches for axiomatizing and formalizing the notion of quantum field theory.

1. A(lgebraic)QFT: this encodes a quantum field theory as an assignment of operator algebras of “quantum observables” to patches of spacetime. Heisenberg picture.
2. F(unctorial)QFT: this encodes a quantum field theory as an assignment of spaces of quantum states to patches of codimension 1, and of maps between spaces of states, namely the time evolution operator, to cobordisms between such patches. Schroedinger picture.