To work out what diagrams describe a particular quantum field theory, we look at the "Lagrangian" function that defines the theory. The Lagrangian has a lot of deep physical meaning, but for our purposes we can think of it as a simple catalog of the particle "fields" in the theory and their possible interactions.

In this simple example, the Lagrangian for
Quantum Electrodynamics (QED), we see two types of particle
fields. Psi represents the electrons, and A_{µ}
is the vector potential of electromagnetism. The vector
potential represents photons in the theory: photons are the
carriers of electromagnetism in addition to being particles of
light. The fact that A_{µ} is a vector (which has
both a length and a direction) corresponds to the fact that
photons are polarized in a specific direction.

So what do the terms represent? They're a bit complicated, but their broad meaning is easy to understand. The first term is the "electron kinetic term": it has two electron (psi) pieces together with a derivative (and some other things). Since derivatives involve changes in functions from point to point, it makes some sense that this term describes an electron starting at one point and moving to another. So Feynman diagrams for QED can include segments like the one at left.

The second term is the "photon kinetic
term": when you multiply it out, you can see that every term
has two photon (A_{µ}) pieces, with derivatives.
This describes a photon starting at one point and moving to
another, with a specified polarization at each end. That means
that Feynman diagrams in QED can include segments like the one
in the middle.

Finally, the last term is the interaction
term, the one that actually describes the electromagnetic
force. It includes the interaction strength (or "electron
charge") *e*, two electron pieces, and a photon piece.
That means that the line segments we saw earlier can join up in
a specific way: two electron legs come together with a photon
(for example, an electron can come in, emit a photon, and go
out).

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Copyright © 2004 by Steuard Jensen.