## Summary

I am now retired, but have an honorary position as a Distinguished Research Fellow in the theoretical physics group.

I have written a book on group theory entitled "*Groups, Representations and Physics"*, published by IOP (now Taylor and Francis). The following image is the cover picture, illustrating the relation between the groups SU(2) and SO(3). The second edition was published in 1998 and contains an additional chapter on the Cartan-Weyl-Dynkin approach to general Lie algebras.

My research is on non-perturbative methods in quantum field theory, and the properties of non-Hermitian, but PT-symmetric, Hamiltonians in quantum mechanics and quantum field theory.

The ideas developed there have recently found very important applications in classical optics, as is explained in my chapter entitled "*PT Symmetry in Optics"* in the book "*PT Symmetry in Quantum and Classical Physics"* (World Scientific, 2019). A more detailed account of my own work is given in my chapter entitled "*Exact Results for a Special PT-Symmetric Optical Potential" *in the book "*Parity-Time Symmetry and its Applications"* (Springer, 2018)

## Publications

### Journals

Jones H, 2021, Comment on 'Solvable model of bound states in the continuum (BIC) in on dimension' (Physica Scripta (2019) 94 105214), *Physica Scripta: an International Journal for Experimental and Theoretical Physics*, Vol:96, ISSN:0031-8949, Pages:1-4

Bender CM, Gianfreda M, Hassanpour N, et al. , 2016, Comment on "On the Lagrangian and Hamiltonian description of the damped linear harmonic oscillator" [J. Math. Phys. 48, 032701 (2007)], *Journal of Mathematical Physics*, Vol:57, ISSN:1089-7658

### Conference

Jones H, Kulishov M, 2021, *Solitons in a PT-symmetric grating-assisted co-directional coupler*, ISSN:1742-6588