What do Feynman diagrams relate to?

(My answer in Quora).

Feynman Diagrams are very useful visual tools (book keeping devices) that have application in understanding the understanding of particles and antiparticles against the critical back drop of time. They are largely employed in the area of Quantum Field Theory as they offer a mechanism of simplifying a complex system into one that is simpler and easier to understand.

Here is an example of a Feynman Diagram

Particles are shown moving forward in time. Antiparticles are indicated by a backward motion in time.(Source: Physics forum)

In this diagram an electron (e negative) interacts with a positron (e positive), The positron is an antiparticle of the electron so it is shown moving backwards. The two particles annihilate each other producing a photo. The photon is indicated by the -sine wave. This in turn becomes a muon-antimuon pair shown by the Greek letters mu negative and mu plus respectively. Again the antiparticle is shown moving backwards in time.

The interesting story about Feynman diagrams is that they were initially resisted by the physics community who preferred equations/graphs to represent the interactions. To his credit Richard Feynman sold the diagrams to the community where they initially known as Feynman-Dyson diagrams (after Freeman Dyson who made a significant contribution to perturbation theory).

Fun fact…Feynman was not the first person to use these diagrams . The accolade for that for goes to the Swiss Physicist Ernst Stueckelberg. Nobel Laureate Murray Gell-Mann regularly referred to these diagrams as Stueckelberg diagrams in honour of their earlier development.

Key methodology followed when drawing a Feynman diagram

1. Electrons are represented with a straight line in the initial state pointing to a vertex. In the final state they point away from the vertex. Positrons as mentioned earlier are depicted going the other way around.
2. Virtual particles are shown with wavy lines.
3. Exchange particles (such as W + Bosons) are shown with Squiggly lines.
4. Time is shown as going from left to right or bottom to top (depending on the diagram)
5. Gluons - particles that mediate the strong nuclear force are shown as spirals.

The diagrams can take on various complexities that can be analyzed using quantum probability calculations.

source: Research gate.

Below is an example showing how Feynman diagrams are applied in Quantum Field Theory.

Source: IB Physics - Particle Physics/

Further reading

https://arxiv.org/pdf/1602.04182.pdf