# Research

## Research interests and topics

The research interests of our group are mostly focussed on mathematical questions in quantum field theory (QFT), and the mathematical structure of QFT models. These are often formulated in the language of operator algebras, in particular von Neumann algebras, and investigated with a range of methods from functional analysis, operator theory, modular theory, complex analysis and representation theory.

Some themes of current research are:

- Construction of interacting quantum field theories from so-called Borchers triples with the help of Tomita-Takesaki theory (see review [L15])
- Twisted Araki-Woods von Neumann algebras ([CL22])
- Scattering theory in QFT, in particular in integrable models ([AL17],[BCL21])
- Structure theory of Borchers triples and non-local examples of QFTs ([LS22])
- Braided structures in QFT and solutions of the Yang-Baxter equation (unitary braidings) ([LPW19],[CL21])
- Non-commutative L^p-spaces and perturbations of KMS states ([C19],[C20])
- KMS states on crossed products and thermal QFT [CGL24]

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