My broad interests over my whole career are the foundations of quantum mechanics and quantum gravity with my present focus being on questions concerning time in quantum mechanics.
I started out in 1983 in the relativity group in Cambridge and worked on quantum cosmology -- the attempt to describe models of the early universe in completely quantum-mechanical terms -- for ten years or more and this area still remains one of interest to me and a source of interesting problems in quantum theory. I subsequentlybecame interested in the decoherent histories approach to quantum theory, which is a novel formulation of standard quantum theory which gives histories a central role. This is of particular interest in quantum gravity, where the notorious problem of time makes it difficult to define a time-evolving state. It also provides an extremely powerful framework in which to address the emergence of classical behaviour from quantum theory, another area on which I have worked for many years, mainly in the context of non-relativistic quantum mechanics.
In the last few years I have worked extensively on aspects of time in quantum mechanics and associated phenomena, including the quantum Zeno effect and also the intriuging phenomenon of backflow -- the (so far unobserved) fact that for a state of purely positive momenta the probability can flow in the opposite direction. I also wrote a paper recentlly offering a sensible interpretation of negative probabilities and another on looking at Fine's theorem, which is essentially the logical converse of Bell's inequalities.
In the next few years I anticipate that I will be continuing to work on time in quantum mechanics, emergent classicality and general issues in the foundations of quantum mechanics.
Janssen O, Halliwell JJ, Hertog T, 2019, No-boundary proposal in biaxial Bianchi IX minisuperspace, Physical Review D, Vol:99, ISSN:2470-0010
Halliwell JJ, 2019, Leggett-Garg tests of macrorealism: checks for noninvasiveness and generalizations to higher-order correlators, Physical Review A, Vol:99, ISSN:1050-2947
Halliwell JJ, Hartle JB, Hertog T, 2019, What is the no-boundary wave function of the Universe?, Physical Review D, Vol:99, ISSN:2470-0010
et al., 2019, Quasiprobability for the arrival-time problem with links to backflow and the Leggett-Garg inequalities, Physical Review A, Vol:99, ISSN:1050-2947
et al., 2018, Damped perturbations in the no-boundary state, Physical Review Letters, Vol:121, ISSN:0031-9007