Paul's research centres around the solution of the quantum-mechanical many-body problem. Mostly this is applied in the case of atomic nuclei, but he has also looked at metal clusters, Bose-Einstein condensates and neutron stars, where similar techniques to those used in nuclear problems may be applied. In the nuclear case he has developed a new approach for going beyond the mean-field approximation based on perturbation theory. Currently he is looking at time-dependent solutions of the Hartree-Fock equations and the connection with the Random-Phase Approximation. In addition, he supports experimentalists at Surrey and elsewhere by applying a variety of models to look at experimental results to help in their interpretation and also in evaluation of the models.
He is also intrerested in the foundations of quantum mechanics and econo- and socio-physics