I am a member of the Mathematical
Physics and Quantum Information group working on quantum theory in flat and curved spacetimes.
My work involves applying rigorous mathematics (particularly functional
analysis) to solve problems of physical interest.
My current research focusses mainly on:
Much of this work uses the powerful framework of algebraic quantum field theory. Kasia Rejzner and I have recently written a pedagogical account Algebraic Quantum Field Theory - an introduction.
- Quantum Energy Inequalities
Unlike most classical forms of matter, quantum fields can have local energy densities that are negative.
However, quantum field theory contains mechanisms (deeply connected to the uncertainty principle) that result in the energy density not being too negative on average. These mechanisms are expressed by results called Quantum Energy Inequalities (QEIs). Much of my work in the period 1998-2008 was devoted to proving QEIs for various different quantum field theories and to examining their consequences and this is still an active area of work. A summary of the area, which also provides a mini-introduction to quantum field theory in curved spacetimes, can be found in my Lectures on Quantum Energy Inequalities and the more recent chapter Quantum Energy Inequalities (in Wormholes, Warp Drives and Energy Conditions, ed. by FSN Lobo).
- Locally covariant quantum field theory
Quantum field theory in Minkowski space depends in many ways on the high degree of spacetime symmetry.
General curved spacetimes lack any symmetry at all, which makes it hard to prove general statements about
general quantum field theories (as opposed to specific models). Work by Brunetti, Fredenhagen and Verch
established a new framework for studying quantum field theory using tools from category theory. I have explored several aspects of this framework, including what it might mean for a theory to describe the same physics in all spacetimes, and a general proof of a Coleman-Mandula theorem for curved spacetimes. For a survey see
Algebraic quantum field theory in curved spacetimes (with R Verch, in Advances in Algebraic Quantum Field Theory, eds. R Brunetti, C Dappiaggi, K Fredenhagen, J Yngvason).
- Measurement theory for QFT
With Rainer Verch, I have developed a general framework for describing measurement interactions in QFT on possibly curved spacetimes. This also provides a local and covariant description of how the state can be updated following a measurement in a consistent way. See
Quantum fields and local measurements and the short summary A generally covariant measurement scheme for quantum field theory in curved spacetimes.
- Singularity theorems under weakened energy conditions
In the 1960's Penrose and Hawking proved that spacetime contains incomplete causal geodesics under quite general conditions, including the classical energy conditions. These results show that black holes and cosmological singularities can inevitable under suitable circumstances. These conditions do not hold in QFT, and our universe does not respect the Strong Energy Condition at the present stage of its evolution. In recent work with Eleni Kontou (building on earlier paper with Greg Galloway) I have proved versions of the singularity theorems that allow for weakened versions of the energy condition, including some that are inspired by QEIs.
Page maintained by CJ Fewster.