On the discrete Dirac spectrum of a point electron in the zero-gravity Kerr-Newman spacetime

Eric Ling (Rutgers University)

03-Feb-2022, 14:30-15:30 (2 years ago)

Abstract: In relativistic quantum mechanics, the point 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 only have a positive electric charge. However, the physical proton also appears to have 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 contains a nonempty 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 yielding hyperfine-like and Lamb shift-like effects.

general relativity and quantum cosmologymathematical physicsanalysis of PDEsdifferential geometry

Audience: researchers in the topic

( video )


JoMaReC - Joint Online Mathematical Relativity Colloquium

Series comments: This monthly online colloquium is meant to be accessible to and informative for mathematicians and mathematical physicists with a background in General Relativity, widely interpreted to include Lorentzian Geometry, and Geometric Analysis of various Partial Differential Equations related to General Relativity.

It is aimed to present motivation and applications of particular results and/or introduce specific subfields, while refraining from too much technicalities.

Organizers: Annegret Burtscher*, Carla Cederbaum, Grigorios Fournodavlos, Edgar Gasperin, Jan Metzger, Anna Sakovich
*contact for this listing

Export talk to