Date of Degree
V. Parameswaran Nair
Elementary Particles and Fields and String Theory
EIH method, anti-de sitter space, particle dynamics, gravity, gauge theory
Following the work of Einstein, Infeld and Hoffmann, we show that particle dynamics in Anti-de Sitter spacetime can be built up by regarding singularities in spacetime manifold as the source of particles.
Since gauge fields play a foundational role in the action, the singularities are chosen to be point-like instantons. Their winding number, defined by an integration on the spheres surrounding those singularities, will turn out to be related to their masses. And their action, derived from the Chern-Simons forms, will be a co-adjoint orbit action, with group element g ∈ SO(4, 2) describing the collective coordinates of the particle.
We also consider bringing the more standard gravitational interactions into the system, which is achieved by combining Chern-Simons action with Einstein-Hilbert action. Interac- tions are proposed to be small perturbations in gauge fields as well as in metric tensors. The equation of motion for perturbed field is obtained and solved. The action, with the solution of perturbed field inserted, approaches Newtonian gravity in non-relativistic limit.
Lei, Jiusi, "Particle Dynamics in Anti-de Sitter Space by EIH Method" (2020). CUNY Academic Works.