My main research interest is quantum field theory in curved spacetime and black hole thermodynamics, focusing especially on mathematical aspects. Hawking’s discovery of black hole radiation (1975) has been a main driving force behind the development of a rigorous framework of generally covariant quantum field theory (QFT), which merges ideas from (algebraic) QFT in Minkowski space and general relativity. In the past few decades, key insights on the implementation of locality and general covariance in a QFT setting have led to an axiomatic description and to a full-fledged perturbative description of generally covariant QFT. This includes a perturbative, background independent description of quantum gravity.
Using advanced methods from analysis, differential geometry and operator algebras I made several contributions to the axiomatic and perturbative approaches by proving rigorous results with physical relevance. I also let the framework shed new light on physical applications: I constructed so-called Hartle-Hawking(-Israel) states, whose existence had been conjectured in 1976 to help understand black hole radiation. At present I am investigating the use of modular operators, which have proven a useful tool in constructive QFT in Minkowski space, and which admit a very well-behaved extension to a generally covariant setting. With these methods I also hope to gain a better understanding of generally covariant thermodynamics. Challenges for the longer term include the rigorous construction of examples of generally covariant quantum field theories satisfying non-linear equations of motion and the relation to non-perturbative approaches to quantum gravity, such as loop quantum gravity and string theory. I believe this field of research still holds a lot of potential to elucidate the many open questions surrounding QFT and quantum gravity.
