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.
Halliwell JJ, Mawby C, 2020, Conditions for macrorealism for systems described by many-valued variables, Physical Review A: Atomic, Molecular and Optical Physics, Vol:102, ISSN:1050-2947, Pages:012209 – 1-012209 – 15
Halliwell JJ, Mawby C, 2019, Fine's theorem for Leggett-Garg tests with an arbitrary number of measurement times, Physical Review A: Atomic, Molecular and Optical Physics, Vol:100, ISSN:1050-2947, Pages:042103 – 1-042103 – 12
Janssen O, Halliwell JJ, Hertog T, 2019, No-boundary proposal in biaxial Bianchi IX minisuperspace, Physical Review D: Particles, Fields, Gravitation and Cosmology, Vol:99, ISSN:1550-2368
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