Relativistic many-body theory

Abstract

Self-consistent field theories have had extensive application in the study of nonrelativistic systems. In the past decade there has been some interest in the use of relativistic self-consistent-field techniques for the study of strongly interacting systems such as finite nuclei and infinite nuclear matter. In nonrelativistic theories the standard analysis involves the determination of a new representation for the Hamiltonian in which the residual interaction admixes no one-particle, one-hole states into the self-consistent ground-state wave function. In lowest-order perturbation theory the next admixtures are of the two-particle, two-hole type. We demonstrate that the relativistic theory can be formulated in a similar fashion. In the relativistic theory the new representation is determined such that the residual interaction does not admix particle-hole states however, here "hole" refers to all occupied states including the negative energy states. Again the corrections to the theory involve the introduction of two-particle two-hole states, where "hole" is understood in the more general sense. In the relativistic theory the specification of the new representation requires the solution of a Dirac-Hartree, Dirac-Hartree-Fock, or Dirac-Brueckner-Hartree-Fock equation, the choice depending upon the nature of the physical system. Once the new representation is found, our techniques allow us to exhibit a useful form for the Hamiltonian of the relativistic system in which the residual interaction between the relativistic quasiparticles is given explicitly. The theory given here is readily extended to the study of finite systems where it provides the basis for a relativistic shell model of nuclear structure.