Renormalization of relativistic self-consistent Hartree-Fock approximation

The renormalization of the relativistic self-consistent Hartree-Fock approximation is restudied. It is shown that the renormalization procedure suggested by Bielajew and Serot can be greatly simplified and the renormalization achieved in a way no more complicated than that of the relativistic self-consistent Fock approximation, if the parameters in the counterterms are allowed to be density-dependent and the renormalization of the tadpole self-energy is treated appropriately. A transformation relation between the four- and three-dimensional representation of the baryon self-energy is presented and a self-consistent Hartree-Fock scheme different from that considered by Bielajew and Serot studied. The renormalized integral equations for the baryon self-energy which includes effects from the Dirac sea are reformulated in a three-dimensional form. Explicit expressions are derived. Received: 29 August 1997 / Revised version: 30 April 1998