The Lamb shift at finite temperature and density

The Lamb shift is a well-known phenomenon that breaks the degeneracy in the 2S1/2 and 2P1/2 energy levels. The currently accepted experimental value is measured to be approximately equal to 1057.862 MHz, or 4.3795×10-6 eV, and theoretically calculated values are very close to this. Theoretical derivation requires a perturbative approach of quantum field theory. Renormalization constants of Quantum Electrodynamics (QED) such as vacuum polarization, self-energy, and radiative corrections to the wave function of the electron contribute to the currently accepted theoretical value of the Lamb shift. We review the structure of the hydrogen atom and the Lamb shift of its 2S1/2 and 2P1/2 energy levels in isolation, and then calculate the temperature and density contributions to the Lamb shift for extremely hot and dense media using the real time approach of QED, which give all the radiative corrections in the form of Masood’s function in many body QED. This result has very important applications in astrophysics and cosmology.