SAMOP 2023 – scientific programme

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Q: Fachverband Quantenoptik und Photonik

Q 19: Precision Spectroscopy of Atoms and Ions II (joint session A/Q)

Q 19.5: Talk

Tuesday, March 7, 2023, 12:00–12:15, F303

Path integral formalism for radiative corrections in bound-state QED — •Sreya Banerjee and Zoltán Harman — Max Planck Institute for Nuclear Physics, Heidelberg, Germany

A step-by-step theory of radiative corrections in bound-state quantum electrodynamics is developed using Feynman’s path integral formalism. As a first step, we derive the free Dirac propagator in spherical coordinates. This is followed by the derivation of the Dirac-Coulomb Green’s function (DCGF) in the Furry picture by reducing it in a basis such that the effective action becomes similar to that of the non-relativistic hydrogen atom. As such, the DCGF is obtained in closed form along with the energy spectrum of the bound states. In the final step, the lowest-order vacuum polarization correction and one-loop self-energy correction to the energy levels of bound electrons are calculated using perturbative path integral formalism. Starting from an interparticle classical action, we arrive directly at the propagators of quantum electrodynamics. The energy level shifts are then calculated from the perturbative shift of poles of the Green’s functions obtained.