A Simple Axiom for Euclidean Quantum Field Theory

Explore a concise yet powerful definition of quantum field theory in this lecture by Werner Nahm from the Dublin Institute for Advanced Studies. Delve into the mathematical formulation of a unitary euclidean quantum field theory as a functor between categories of Riemannian manifolds and Hilbert spaces. Examine how this axiom extends to non-unitary cases using self-dual Banach spaces. Discover how the fundamental properties of the categories, including continuity, monoidal structure, and self-adjointness, are preserved by the functor. Gain insights into how this mathematical framework gives rise to the familiar physics of quantum field theory, bridging the gap between abstract mathematical concepts and physical phenomena.