Snowmass White Paper: The Quest to Define QFT

Understand

This article provides a review of the literature on rigorous definitions and constructions in Quantum Field Theory, spanning the period of seven decades.

• Comparing with the ideas and constructions found in the modern physics literature, we conclude that none of the existing systems of QFT axioms can cover all the physical situations.
• Therefore, it is still an outstanding open problem to formulate a complete definition of QFT.
• We argue that the question is of relevance for both physicists and mathematicians.