Probabilistic interpretation of quantum field theories
Martin Hairer
TL;DR
This paper introduces the mathematical foundations of quantum field theories, focusing on Liouville theory and Segal's axioms, highlighting recent rigorous constructions in 2D conformal field theory.
Contribution
It provides an accessible overview of the rigorous construction of Liouville theory and its relation to Segal's axioms for conformal field theories.
Findings
Rigorous construction of 2D Liouville theory
Connection between free fields and Segal's axioms
Clarification of concepts in quantum field theory
Abstract
In this note we provide a gentle introduction to the concepts and intuition behind the recent breakthrough results on the mathematically rigorous construction of a non-trivial 2D conformal field theory, namely the so-called Liouville theory. This gives us the opportunity to review Segal's axioms for conformal field theories and to discuss in some detail how the free field fits into them.
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Taxonomy
TopicsQuantum Mechanics and Applications