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Dezign
(18 Aug. 2023)

 

ill title  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:

  1. 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.
  2. Cosmological implications of a diffeomorphism field interacting with electromagnetic radiation and in particular the microwave anisotropy.
  3. Studying sterile neutrinos coupled to the diffeomorphism field as dark matter candidates.