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.
et al., 2017, Real no-boundary wave function in Lorentzian quantum cosmology, Physical Review D, Vol:96, ISSN:2470-0010
Halliwell JJ, 2017, Comparing conditions for macrorealism: Leggett-Garg inequalities versus no-signaling in time, Physical Review A, Vol:96, ISSN:2469-9926
Halliwell JJ, 2017, Incompatible multiple consistent sets of histories and measures of quantumness, Physical Review A, Vol:96, ISSN:2469-9926
Halliwell JJ, 2016, Leggett-Garg inequalities and no-signaling in time: A quasiprobability approach, Physical Review A, Vol:93, ISSN:2469-9926
Halliwell JJ, 2016, Leggett-Garg correlation functions from a noninvasive velocity measurement continuous in time, Physical Review A, Vol:94, ISSN:2469-9926