Dynamical gauge fields are a fundamental concept of high-energy physics. However, learning about them typically takes enormous amounts of time and effort. As such, they are typically a bit mystical to students (including me) of other fields of physics like condensed-matter or AMO. Here, we will give a simple introduction into some of the concepts that might allow for the quantum simulation of these theories with ultracold atomic gases.The reader should know about second quantization and the basics of quantum mechanics as the arguments are based on this formalism.
In this lecture we will discuss some basic properties of the Helium atom. We will introduce first some useful notations for the specific Hamiltonian at hand. Then we will focus on the important consequences played by the electron-electron interaction on the spin structure and the level scheme of the system. Finally, we will introduce the variational method for the estimation of the ground state energy.