Oct 25, 2026 · 17 min · 12 segments
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Matt O'DowdHost
For this to be interesting, the electric and electromagnetic fields need to interact.

Particle slash field interactions are represented as a vertex, a point where the lines representing the different particles come together.

It turns out that there's only one vertex that's possible in QED, one with an arrow pointing in an arrow pointing out, and a single photon connection.

Oriented like this, with time increasing upwards, this vertex represents an initial electron that emits a photon, after which both particles move off in opposite directions.

But if we rotate this vertex so that photon is coming in from below, we have a picture in which an electron absorbs that incoming photon.

Rotate again, and the picture is of a photon coming in and giving up its energy to produce an electron-positron pair, a process we call pair production.

Rotate again, and now we have a positron absorbing a photon and a positron emitting a photon, and finally, an electron and a positron annihilating each other to produce a photon.

Energy and momentum conservation requires that particles not just vanish or appear from nothing, which guarantees that if something goes in, then something else must come out.

If one electron or positron goes in, then one electron or positron, respectively, must leave.

If an electron and positron both go in, then their charges cancel, so a zero-charged photon must leave.

Similarly, if a photon creates a negatively charged electron, it must also create a positively charged positron.

There are other more complex ways in which ingoing and outgoing particles can balance charge, but as we'll see, all of these can be built up from this one vertex.

For this to be interesting, the electric and electromagnetic fields need to interact.

Particle slash field interactions are represented as a vertex, a point where the lines representing the different particles come together.

It turns out that there's only one vertex that's possible in QED, one with an arrow pointing in an arrow pointing out, and a single photon connection.

Oriented like this, with time increasing upwards, this vertex represents an initial electron that emits a photon, after which both particles move off in opposite directions.

But if we rotate this vertex so that photon is coming in from below, we have a picture in which an electron absorbs that incoming photon.

Rotate again, and the picture is of a photon coming in and giving up its energy to produce an electron-positron pair, a process we call pair production.

Rotate again, and now we have a positron absorbing a photon and a positron emitting a photon, and finally, an electron and a positron annihilating each other to produce a photon.

Energy and momentum conservation requires that particles not just vanish or appear from nothing, which guarantees that if something goes in, then something else must come out.

If one electron or positron goes in, then one electron or positron, respectively, must leave.

If an electron and positron both go in, then their charges cancel, so a zero-charged photon must leave.

Similarly, if a photon creates a negatively charged electron, it must also create a positively charged positron.

There are other more complex ways in which ingoing and outgoing particles can balance charge, but as we'll see, all of these can be built up from this one vertex.
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