Mathematical Physics
The Mathematical Physics group performs research into problems related to physics, including operator algebras, path integrals and quantization.
Group Members
Research Interests
Hendrik Grundling works on mathematical physics problems in the two areas of quantum field theory and quantization theory. In quantum field theory he is concerned with issues arising from gauge theory and in particular the problem of quantum constraints. The analysis is done in the context of operator algebras, so he is also concerned with problems in that area as well as with the representations and actions of groups which are not locally compact. In quantization theory, he studies the existence and uniqueness of quantizations of Poisson algebras associated with simple manifolds other than the plane.
Brian Jefferies is interested in the mathematics of path integrals and their connection with stochastic equations and measure theory. As well as their pervasive use in quantum physics, path integrals in the guise of a heuristic calculational tool are appearing in ever-increasing areas of mathematics, such as knot theory and low dimensional topology. He is the author of "Evolution Processes and the Feynman-Kac Formula", published by Kluwer in 1996. His interests overlap with the harmonic analysis and functional analysis groups.
Jonathan Kress works on classical and quantum superintegrable systems. These are natural Hamiltonian systems having the maximum number of independent symmetries and as a result possess many useful and interesting properties. The most celebrated examples are the harmonic oscillator and Kepler-Coulomb system, but recently many more examples have been found.
John Steele's interests are in the area of General Relativity, particularly in exact solutions of the Einstein Field Equations, their symmetries and interpretation. He is also interested in geometric aspects of mathematical physics and the history of mathematical physics.
Peter Donovan, now semi-retired, has publications in algebraic geometry (localisation at fixed points), algebraic topology (related to geometrical physics), representation theory (including the first non-trivial progress towards a key finiteness conjecture in the modular representation theory of finite groups), homological algebra and the insecurity of Japanese naval ciphers in WW2. Currently his interests are returning to modular representation theory and geometrical physics.
