Research Efforts
The Coadjoint Representations and Projective
Geometry: The coadjoint representation of the
Virasoro algebra and Affine Lie algebras have provided insight
into the nature of classical and quantum gravity in the
absence of curvature especially in two and three space-time
dimensions. In higher dimensions we can identify the
coadjoint elements of the affine Lie algebra as Yang-Mills
fields and recently the coadjoint representation of the
Virasoro algebra as a projective connections. Because of
this identification, we can build general coordinate invariant
actions directly in four-dimensions that exhibit new
gravitation fields that couple to matter and the metric.
Some of the problems being studied are:
- Dark Energy and Dark Matter originating from the projective representations in 4 dimensions - the diffeomorphism field here acts as a dynamical projective Schouten tensor. The energy-momentum tensor is modified in the presence of dynamical projective geometries suggesting dark energy candidates.
- Cosmological implications of a diffeomorphism field interacting with electromagnetic radiation and in particular the microwave anisotropy.
- Studying sterile neutrinos coupled to the diffeomorphism field as dark matter candidates.