I am particularly interested in new approaches to the problem of rigorously constructing quantum field theory models. A novel line of research addresses this question via operator-algebraic deformations of quantum field theories, a topic also connected to non-commutative geometry and quantum field theory on non-commutative spaces. Steve Summers has written a nice overview over the 2009 status of “constructive algebraic quantum field theory” here: math.ufl.edu/~sjs/construction.html.
Title: Deformations of Operator Algebras and the Construction of Quantum Field Theories
Event: Algebraic Quantum Field Theory – the first 50 Years
Date: July 30, 2009
Title: Yang-Baxter Representations of the Infinite Symmetric Group
Event: 40th LQP Workshop "Foundations and Constructive Aspects of QFT"
Date: June 24, 2017
Title: Sigma Models in Algebraic Quantum Field Theory
Event: Local Quantum Physics and beyond - In memoriam Rudolf Haag
Date: September 27, 2016
Title: Localization in Nets of Standard Spaces
Event: Algebraic Quantum Field Theory - Its status and its future
Date: May 21, 2014
- Title: Deformations of Operator Algebras and the Construction of Quantum Field Theories