Feynman Diagrams

Introduction

Feynman Diagrams are pictorial representations of the interactions of subatomic particles

For example, this shows a Feynman Diagram of beta (β-) decay (see our notes on nuclear equations if you have not done so already):

Feynman equations

Usually, Feynman Diagrams are read from left to right

So, here, we can see a neutron decaying into a proton and a W- exchange particle, which subsequently decays into an electron and an electron anti-neutrino

Thus, this is showing a weak interacting and can be written as an equation as follows:

Feynman equations

The big advantage of Feynman Diagrams is that it not only tells you what goes into the interaction and what comes out, but also what goes on during the interaction itself

Rules of Feynman Diagrams

Particles are represented using straight lines with arrows on them

Exchange particles are represented using wavy lines

They usually move from left to right, with the first action happening on the left and the last happening on the right (although this isn't always the case, with some moving vertically instead)

Particle creation and annihilation occurs where the lines come together

Exchange particles usually move left to right unless there is an arrow above the wavy line that indicates it is moving in a different direction

Examples of Feynman Diagrams

Two Electrons Scattering Off Each Other

Feynman diagram for electron Scattering

In this diagram we can see that two electrons meet, exchange photons, and then scatter away from each other

The photon symbol (γ) shows that this is an example of electromagnetic interaction

β+ (positron) radioactive decay

Feynman diagram for positron radioactive decay

In this diagram, we can see a proton decays into a neutron and a W+ exchange particle, which subsequently decays into a positron and an electron neutrino

This is an example of weak interaction (like the β- decay, above)

The equation for this radioactive decays is as follows:

Feynman diagram for positron radioactive decay

Note: β- decay is negative so it involves e-, an anti-neutrino and W-, whereas β+ decay is positive so involves e+, a neutrino and W+

Electron Capture

Feynman diagram for electron capture

This is also an example of weak interaction

Through electron capture, an electron is absorbed by a proton within a nucleus

The proton decays into a neutron and a W+ exchange particle. The W+ exchange particle interacts with the electron forming an electron neutrino

  • As the proton acts on the electron, the exchange particle moves from left to right

The equation for this is as follows:

Feynman diagram for electron capture

Electron-proton collision

Feynman diagram for Electron-proton collision

When a proton and an electron collide at very high-speeds they will transfer a W- particle, again indicating a weak interaction

The proton decays into a neutron and the electron decays into an electron neutrino

  • This time, as it is the electron that is colliding with the proton, the exchange particle moves from right to left

The equation for this is as follows:

Feynman diagram for Electron-proton collision

Proton-Neutron bound by a gluon

Feynman diagram for a proton-neutron bound by a gluon

As a gluon exchanges between protons and neutrons continuously, it binds them together

This symbol for this exchange particle (i.e. the gluon) is different than that used for other exchange particles

This is an example of strong interaction