Relativistic Calculation Mathod for higher order correlation for molecles and atoms

Abstract

We propose Atomic Schwinger-Dyson formalism(ASD method) and renormalization under an external field in this paper, which is the nonperturbative and finite relativistic quantum field theory for a finite baryon and electron density. ASD can be applied to many of electron systems and electron matters. ASD consists of coupled Dyson equations of electrons and photons. It is shown that an electromagnetic field of ASD is separated into two parts, which are a mean field (classical field) and a fluctuation (quantum field). Because it includes self-energies in nonerturbative way, higher-order correlations beyond Hartee-Fock approximation are taken into account. In order to prepare for numerical calculations, we give a new explicit expressions of photon self-energies and electron self-energy, which are introduced for photons and electrons based on the particle-hole-antiparticle representation (PHA) of Atomic Schwinger-Dyson formalism (ASD). The PHA representation describes exactly the physical processes such as particle-hole excitations (electron-hole) and particle- antiparticle excitations (electron-positron).