User:Colin Kiegel~enwikibooks

I'm going to contribute something about gauge theory. But I'll keep it here, until it's finished.

Dirac Theory
Dirac in 1928 successfully established a theory to describe relativistic free electrons (or any spin-1/2 particle). Within the framework of Lagrangeformalism he derived

$$\mathcal{L}_D = \bar{\psi}(x)(i\gamma^\mu \partial_\mu - m) \psi(x)$$

where

$$\bar{\psi} := \psi^\dagger \gamma^0$$

$$\gamma^0:=\left( \begin{array}{cc} \mathbb{E}_2 & \\ & -\mathbb{E}_2\\ \end{array}\right)$$

$$\gamma^i:=\left( \begin{array}{cc} & \sigma^i \\ \sigma^i & \\ \end{array}\right)$$

We will now start with Diracs Theory of a free