The potential of gauging phase space dynamical symmetries as a principle for generating interactions is explored
Combining complementary approaches to quantisation, exploration of integrability issues in quantum dynamics and noncommutative geometric structures
External collaborators: M. Norbert Hounkonnou (ICMPA-UNESCO Chair, UAC, Benin) Calvin Matondo Bwayi (UNIKIN, DRC).
Extensions to the supersymmetric context of the Moyal non-commutative plane are being considered from different perspectives.
By emphasizing the relevance of topology in nonperturbative gauge dynamics in the presence of nontrivial space(time) topology, develop gauge invariant physical tools to approach the nonperturbative dynamics of such systems in approximation schemes. In an initial study, QED in lower dimensions is considered in detail.
Development of nonperturbative quantisation techniques of gauge theories (Yang-Mills, topological, gravity) and their application to particle physics and quantum field theory at finite temperature (in particular, within the context of superconductivity). Exploration of the consequences of noncommutative geometry in the search for the unification of the fundamental interactions (M-theory and superstrings, quantum gravity).
External collaborators: Frederik Scholtz (National Institute for Theoretical Physics, NITheP, South Africa); Hendrik Geyer (Stellenbosch Institute for Advanced Study, STIAS; University of Stellenbosch, South Africa); Fritz Hahne (African Institute for Mathematical Sciences, AIMS, South Africa); M. Norbert Hounkonnou (International Chair in Mathematical Physics and Applications, ICMPA-UNESCO Chair, Benin); Calvin Matondo Bwayi (University of Kinshasa, Kinshasa, Democratic Republic of Congo); Habatwa Mweene (University of Zambia, Lusaka, Zambia); John R. Klauder (University of Florida, Gainesville, USA); Chris Hamer (University of New South Wales, Sydney, Australia); Peter Jarvis (University of Tasmania, Hobart, Australia).
Quantum diffeomorphic gauge invariance and the total cosmological constant, inclusive of the quantum fluctuations of the gravitational field
Theoretical and experimental study of superconductivity in extremal regimes (spatial and temporal, and in the presence of electric fields), aiming towards the development of nanoscopic particle detectors
External collaborators: Vincent Bayot (CERMIN, UCL).
We are beginning to investigate the possibility of using finite sized matrices to describe a non-commutative three dimensional ball.
The connections between topology in space(time) and in field configuration space and the non-perturbative dynamics of general gauge theories, inclusive of mass generating mechanims, are being studied.
