## Summary

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.

## Publications

### Journals

Mawby C, Halliwell JJ, 2023, Leggett-Garg violations for continuous-variable systems with Gaussian states, *Physical Review A*, Vol:107, ISSN:2469-9926

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