Recall from last lecture:

Rules for Drawing Feynman Diagrams (version one)

  1. The horizontal direction is the horizontal direction, increasing from left to right. The vertical direction represents all other spatial directions. The left side of the diagram represents the initial state, and the right side represents the final state. (Again, some authors draw time in the vertical direction, in which case you can rotate the drawing clockwise by 90° to get our convention.)
  2. Fermions are drawn as continuous, solid lines. A fermion line can end only in the initial or final states (left or right side of the diagram).
  3. Bosons are drawn as dashed lines, wavy lines, or loopy (helix or spring-like) lines. Photons are represented by wavy lines, gluons by loopy lines, and Z° or W± by either wavy lines or dashed lines.
  4. Lines should be labeled to avoid confusion.

This is enough to start with, let's use these to look at a more complex interaction.

Quantum Chromodynamics (QCD)

The strong force is mediated by a massless boson called the gluon. The basic interaction vertex of gluon with two quark lines looks nearly identical to the interaction vertex of a photon with two charged particles. Instead of coupling to charge, the gluon couples to color. There are three colors -- I will use red, green, and blue -- but they usually don't get mentioned in diagrams because the physical particles, the hadrons, are colorless.

The fact that there are three colors is experimentally verified in a number of ways. The classic proof is the existence of the W± baryons consisting of 3 strange quarks in an S-wave configuration so that the particle has spin=½.

The Weak Force

The Yukawa Theory of Quantum Exchange

This section and the next present a "hand waving" argument for the form of the propagator expression. The following is my summary of the argument.

The binding of protons and neutrons in a nucleus was postulated to be due to a short range strong force with a potential of the form:

U(r) = (g0/4pr)e-r/R
where R can be related to a mass by
R = hbar/mc.
Without the exponential term, the form of the potential is like the electrostatic potential U = Q/4pr, leading us to interpret g0 as a sort of "strong force charge". Now, we simply call g0 the strong coupling constant. The mass in R is interpreted as the mass of the boson exchanged between two particles, and, for m>0, makes the force short range. Yukawa's theory now is seen as an approximation to the true effects of the strong force with massless gluons.

The Boson Propagator

Jump ahead by a decade and this idea resurfaces.

Copyright © Robert Harr 2003