In this work, we consider the generalized quantum electrodynamics proposed by Podolsky in Heisenberg picture via Källén methodology. We investigate the effects of higher-order derivatives to understand the qualitative and quantitative aspects of vacuum polarization. In addition, the most general structure of induced current and polarization tensor that emerge naturally by a perturbative scheme “à la” Källén is also obtained. Afterward, we discuss the physical implication of charge renormalization in the perspective of unitary and stable Podolsky theory.
The discrepancy between theoretical and experimental X-ray energies in muonic atoms is reviewed. We give brief descriptions of all the known corrections, such as finite size, vacuum polarization and electron screening, and attempt to estimate the theoretical errors. The discrepancy is found to remain at the two standard deviation level in eight transitions, and we offer some speculations on the resolution of the problem.
Semi-analytic approach to higher-order corrections in simple muonic bound systems: Vacuum polarization, self-energy and radiative-recoil