Henning Bostelmann

A Brief Introduction to Axiomatic Quantum Field Theory

Abstract:

Quantum field theory aims at unifying quantum theory with the principles of (special) relativity. Its consistent mathematical description, beyond the level of formal perturbation theory, remains a challenging problem. On Minkowski space, two mathematical frameworks have emerged for the description of quantum field theory: First, the Wightman axioms, which focus on the more familiar notion of quantum fields and deal with unbounded operators; second, the more abstract Haag-Kastler setting, which takes algebras of bounded operators as its fundamental objects. This lecture gives a brief introduction to each of the two frameworks, motivates their conceptual foundations, and sketches basic techniques and results. Also, we discuss how to pass from the Wightman to the Haag-Kastler setting and vice versa.