Algebraic quantum field theory

QFT is an outstandingly successful description of matter at short distance or high energy scales. However, its mathematical status is problematic: while it is possible to write down a short list of properties (or axioms) that seem reasonable assumptions on any QFT, no one has succeeded in giving a mathematically precise construction of a QFT on four-dimensional Minkowski spacetime that obeys all the assumptions and has nontrivial interactions.

This may indicate that we do not fully understand what QFT really is and that our current understanding is tied too closely to classical field theory.

Algebraic QFT (AQFT) focuses attention on the algebras of local observables with very few additional assumptions. It has been very fruitful in both understanding the general structures of QFT and in developing new mathematics in operator algebra theory.

Our work particularly focuses on:

• new constructions of quantum field theory (QFT) in low dimensions
• new mathematical frameworks for perturbative constructions of interacting theories
• the general theory of measurement for quantum fields
• applications of higher structures (categories, operads, groupoids) in QFT.

AQFT also provides a viewpoint that is ideal for studying QFT in curved spacetimes.