QLunch: Eric Ling

Speaker: Eric Ling

Title: On the hydrogen problem with a zero-gravity Kerr-Newman source for the proton

Abstract: In relativistic quantum mechanics, the discrete spectrum of the Dirac Hamiltonian with a Coulomb potential famously agrees with Sommerfeld’s fine structure formula for the hydrogen atom. In the Coulomb approximation, the proton is assumed to have a positive electric charge but no magnetic moment. However, the physical proton also has a magnetic moment which yields a hyperfine structure of the hydrogen atom that’s normally computed perturbatively. Aiming towards a non-perturbative approach, Pekeris in 1987 proposed taking the Kerr-Newman spacetime with its ring singularity as a source for the proton’s electric charge and magnetic moment. Given the proton’s mass and electric charge, the resulting Kerr-Newman spacetime lies well within the naked singularity sector which possess closed timelike loops. In 2014 Tahvildar-Zadeh showed that the zero-gravity limit of the Kerr-Newman spacetime (zGKN) produces a flat but topologically nontrivial spacetime that’s no longer plagued by closed timelike loops. In 2015 Tahvildar-Zadeh and Kiessling studied the hydrogen problem with Dirac’s equation on the zGKN spacetime and found that the Hamiltonian is essentially self-adjoint and found a single bound state for the discrete spectrum. In this talk, we show how their ideas can be extended to classify the discrete spectrum completely and relate it back to the known hydrogenic Dirac spectrum but now yielding hyperfine-like and Lamb shift-like effects.