Professor Paul Strange

Paul Strange is an Emeritus Professor of Theoretical Physics. For much of his career, Paul's research has been focused on condensed matter physics. This has taken two forms. On the one hand, he has been interested in rare earth materials and their properties and on the other, he has looked at relativistic effects in materials. In recent times, he has concentrated on mathematical physics with interests in exactly soluble models within the relativistic quantum theory, superoscillations, knotted electromagnetic fields and non-conventional forces such as curl forces and Lipkin’s zilches.  

All of Paul's current research is in mathematical physics. He has a number of current projects: 

Model Calculations within Relativistic Quantum Theory

Paul wrote a book on relativistic quantum theory (see publications) and he always has ideas for model calculations within this theory. Often they don’t amount to much, but sometimes they yield considerable insight. Recent successes include:

• the observation that quantum backflow can occur in a system with angular momentum, leading to it being long-lasting;
• the discovery of some novel beam-like solutions of the Dirac equation;
• an understanding of the relativistic theory of quantum revivals;
• looking at the Dirac oscillator from a rotating frame of reference.

Currently, he is looking at the spin of Dirac wavepackets from the point of view of an observer in a rotating frame of reference.

Superoscillations

Superoscillations can exist in a function that is band-limited where in some regions of space the function can oscillate arbitrarily faster than its most rapidly varying Fourier component. We have built a wavepacket from harmonic oscillator eigenfunctions and developed a theory of its evolution. Current projects in this area include:

• Looking at the evolution of superoscillations in a relativistic wavepacket;
• simulating natural oscillations in two dimensions and examining the statistical probability of superoscillations occurring.

Knotted Electromagnetic Radiation

Electromagnetic radiation is well described by Maxwell’s equations of classical electromagnetism.  In recent years some exotic solutions of Maxwell’s equations have been (re)discovered where the light appears to knot around itself. Such knotting is found to be topologically stable.

We are examining the properties and underlying topology of these solutions. In particular, we are examining Lipkin’s zilches, little known conserved quantities in electromagnetism and what they can tell us about these solutions. We are also looking into suggesting ways of generating such solutions experimentally.

Curl Forces

Curl forces are forces that cannot be derived as the gradient of a potential and whose curl is not equal to zero. An example is the forces felt by nanoparticles in the presence of electromagnetic fields. A robust classical theory of these forces exists, although there are still some gaps in the theory to fill in. There is no quantum theory of such forces, so we are attempting to develop one.