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);
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);
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
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.
In this project, we study a deformation of the path integral introducing a new time scale. This deformation is inspired by Klauder's path integral construction using a Riemannian metric on phase space. The introduction of this new time scale leads to a complex Landau problem, non commutative geometry and non unitarity effects.
The potential of gauging phase space dynamical symmetries as a principle for generating interactions is explored
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.
This project is concerned with the construction the polarization tensors for (some of) the Fuzzy Grassmanians. We will then consider the Dirac operator and spinors for these spaces in the compact formalism recently introduced for the complex projective spaces. We will also consider structures.