Feynman Diagrams

Feynman diagrams are mathematical tools in order to describe QFT interactions in a more efficient way. They were created by Richard Feynman, one of the most influential physicists of the 20th century. It is important to know that Feynman diagrams are idealized interactions between particles, and calculating the real interactions is very complicated.

Instead of electrons being repelled because they both have the same charge, as shown:

You can describe the same interaction with the exchange of a virtual photon.

In the Feynman diagram, the photon is represented by gamma (the one that looks like a y).

That is the premise of Feynman's diagrams. Let's go over the basics of how to read them.

This is a basic QED interaction. In it, an electron and positron (the antiparticle for the electron) annihilate and emit a photon. We know that the positron is a positron because of the direction the arrow is facing. Mathematically, positrons seem to have backward time. As a result, If the arrow is against the direction of time in the diagram, then it is an antiparticle.

This interaction can also be rotated in order to describe different scenarios. For example, this diagram shows an electron emitting a photon and moving in a different direction.

This one shows a photon splitting into an electron and positron.

All the other diagrams for the electromagnetic field can be built off this interaction. This is because conservation laws such as conservation of energy or momentum make sure that if something goes into the interaction, what comes out must conserve values. One example of such an interaction looks like this:

This example is the one used in: https://www.youtube.com/watch?v=fG52mXN-uWI

You can see the basic vertex in every part of this diagram. In other words, for every vertex, there is a photon, an arrow pointing in, and an arrow pointing out. In this way, there are an infinite amount of combinations of interaction. However, the more vertices, the less likely the interaction occurs.

The diagram itself is defined by the particles going in and the particles going out. Anything other than those is virtual particles. The purple highlighted particles are the real particles, and the yellow highlighted particles are virtual ones.

Here are some diagrams for the strong force. The corkscrew lines represent gluons.