Study of Simulation Method of Time Evolution in Rigged QED

TL;DR

This paper proposes a new simulation method for time evolution in Rigged QED, expanding field operators and deriving evolution equations, demonstrated through numerical simulation of a hydrogen atom's electron charge density.

Contribution

It introduces a novel approach to simulate time evolution in Rigged QED by expanding field operators and deriving approximate evolution equations for electrons and nuclei.

Findings

Derived time evolution equations for field operators.

Proposed an approximation method using density matrices.

Numerically simulated electron charge density in hydrogen atom.

Abstract

We discuss how we formulate time evolution of physical quantities in the framework of the Rigged QED (Quantum Electrodynamics). The Rigged QED is a theory which has been proposed to treat dynamics of electrons, photons and atomic nuclei in atomic and molecular systems in a quantum field theoretic way. To solve the dynamics in the Rigged QED, we need different techniques from those developed for the conventional QED. As a first step toward this issue, we propose a procedure to expand the Dirac field operator, which represents electrons, by the electron annihilation/creation operators and solutions of the Dirac equation for electrons in nuclear potential. Similarly, the Schrodinger field operators, which represent atomic nuclei, are expanded by nucleus annihilation/creation operators. Then we derive time evolution equations for these annihilation and creation operators and discuss how time evolution of the operators for physical quantities can be calculated. In the end, we propose a method to approximate the evolution equations of the operators by the evolution equations for the density matrices of electrons and atomic nuclei. Under this approximation, we carry out numerical simulation of the time evolution of electron charge density of a hydrogen atom.