On relativistic approaches to the pion self-energy in nuclear matter
We argue that, in contrast to the non-relativistic approach, a relativistic evaluation of the nucleon--hole and delta-isobar--nucleon hole contributions to the pion self-energy incorporates the s-wave scattering, which requires a more accurate evaluation. Therefore relativistic approach containing only these diagrams does not describe appropriately the pion self-energy in isospin symmetric nuclear matter. We conclude that, a correct relativistic approach to the pion self-energy should involve a more sophisticated calculation in order to satisfy the known experimental results on the near-threshold behaviour of the pion-nucleon (forward) scattering amplitude.