Mathematical Physics Group
The mathematical physics team has strength in diversity and is well recognised internationally. Research involves the mathematical physics of microscopic particles (on subatomic, atomic and molecular scales), mesoscopic structures (condensed matter and networks) and macroscopic entities in the Universe (such as the large-scale structure of space-time). A unifying theme is statistical physics, which link these various structures in very fundamental ways through phase transitions and symmetry breaking, concepts which originated in condensed matter physics.
The boiling of water, the magnetization of iron, the formation of ordered phases in liquid crystals and the origins of mass through the Higgs mechanism are all examples of phase transitions. Iron, for example, loses its magnetic properties when heated above a certain 'critical' temperature. Transitions like this one are common in nature. Indeed, as the early universe cooled, after the big bang, it underwent a sequence of similar phase transitions. The various forces that act on subatomic particles of matter changed in very profound ways.
The statistical physics theme of the Mathematical Physics group is strengthened through established links with collaborators nationally and internationally, including at Cracow, Freiburg, Heriot-Watt, Leipzig, Linz, Lviv, Mainz, Nancy, Queen Mary (London) and Trinity College Dublin. Links are further maintained through organisation of conferences, such as the 16th Workshop on Lattice Field Theory and Statistical Physics.
Christian von Ferber's interests extend from the statistical mechanics of macromolecules to the vulnerability of public transport networks. Macromolecules or polymers are ubiquitous in nature and as synthetic materials. Well known examples are polyethylene (PE) and polyvinyl-chloride (PVC) while the DNA is probably the best known biological macromolecule. These molecules constitute very long chains of up to 10,000 and more units. Christian's research in this area focuses on the statistics, symmetries and dynamics of these systems using renormalization group methods as developed in high energy physics as well as computer simulations. Besides this he also pursues studies in other areas of complex systems like self-assembling materials, diluted magnets, hard body mixtures, percolation, and large complex networks.
Ralph Kenna's research concerns the physics and mathematics of phase transitions, both in statistical physics and in lattice field theory. In the latter, space-time itself is discretized so that it forms a crystal, like a condensed matter system. Classical and quantum theories constructed in such finite-sized systems, are well-defined and are amenable to powerful perturbative and non-perturbative methods. Such methods are both developed and applied in Coventry.
Rob Low is interested in general relativity. In particular, he researches the causal and large-scale structure of space-time. This aspect of the structure of space-time is conformally invariant, and is intimately tied up with the light cones and light rays, or null geodesics in space-time. Much of his research has involved trying to understand the causal structure of space-time by considering the space of null geodesics, and structures on that space. He also works in other aspects of mathematical physics including phase transitions in liquid crystals.
