RELATIVISTIC QUANTUM FIELD THEORY FOR CONDENSED SYSTEMS-(III): AN EXPLICIT EXPRESSION OF ATOMIC SCHWINGER–DYSON METHOD

Abstract

A new explicit expressions of self-energies Πμν and Σ 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). The self-energy Σ includes both the quantum component and the classical component (classical external field and Coulomb's field), which are divided into the scalar part Σs and 4-dimensional vector parts Σ0, Σj. The electron propagators are composed of the particle part, hole part and antiparticle part in PHA representation. The general representation of photon self-energy Πμν with 16 elements is expressed in terms of only two components (transverse and longitudinal) Πt and Πl. The general form of the photon propagators are written in terms of free propagator D0 and two independent propagators Dl and Dt, which include two independent photon self-energies. The tensor part of the electron self-energy does not appear in ASD formalism which makes perfectly the closed self-consistent system, when we take the bare vertex approximation, Γμ→γμ.