Theory of Quantum Electrodynamical Self-consistent Fields

TL;DR

This paper develops a formal framework for quantum electrodynamical self-consistent fields, deriving relativistic Hartree-Fock and related theories for atomic and molecular systems using Green's functions and operator formalism.

Contribution

It introduces a comprehensive formalism for QED self-consistent fields, including derivations of relativistic Hartree-Fock, time-dependent Hartree-Fock, and RPA theories.

Findings

Derived QED Hartree-Fock theory using Green's functions

Constructed a relativistic Hamiltonian with creation-annihilation operators

Discussed potential applications and future developments

Abstract

To obtain the basis for combining various many-body techniques to QED in a consistent manner, we investigate the theory of quantum electrodynamical self-consistent fields. The reserch interest was born mainly of the electronic structure theory, thus we consider of atomic and moleculer systems as our main subjects. But the formalism is more fundamental. First, we derive the quantum electrodynamical Hartree-Fock theory by using the Green's function method. Then we construct a relativistic Hamiltonian written by creation-annihilation operators for electron and positron in a general form, and check that it reproduces the Hartree-Fock theory. We use this Hamiltonian to derive the time-dependent Hartree-Fock theory and random phase approximation, in the operator formalism. The relativistic Slater determinant of the Thouless parametrization is also used. Finally we discuss the applications and futher possible developments.