jheimann@bbncc5.UUCP (John Heimann) (10/10/85)
As I recall (and it's been a while) the thing to remmeber about Feynman diagrams is that they are not pictures, but rather very suggestive notational devices. A Feynman diagram is basically a shorthand way of writing an integral equation for certain functions called propagators. Here's where my memory gets fuzzy, but propagators are basically Green's functions, which (as everyone who has suffered through potential theory knows) represent the "potential" at a point y caused by a source at point x. In other words, they represent the influence that a particle at one point has one a particle at another point. This is not "action at a distance", however, since interactions are mediated by fields, and the Green's functions include time in the definition of "point y" or "point x" so that causality isn't violated. It is often convenient to think of interactions as being mediated by virtual particles, but since these particles are described by field equations their introduction should be thought of as a conceptual aid rather than being central to the physics. Given a Feynman diagram one can write down the integral equation for an interaction. For instance (here's where my memory gets really fuzzy), I believe that the number of cross lines in the diagram represents the order of the term in the series expansion of the Green's functions which the diagram represents (one typically solves integral field equations by expanding the Green's functions in a series, even if one suspects that the series has no chance of convergence). The nice thing about Feynman diagrams is that they actually look like what you might think was going on in the interaction if you had to visualize it. If they were just pictures and had no mathematical significance they might still have been useful, but it certainly wouldn't have taken Feynman to think of them. In other words, the Feynman diagram for e-e- scattering shouldn't be interpreted as a literal picture, i.e. as a drawing of the actual trajectories of particles involved in the interaction. The squiggly line between the two lines for the e-'s can be thought of as a virtual photon mediating the interaction, but that interaction can be attractive or repulsive. It doesn't represent the path of a photon flying off of one e- and bashing into the other, providing repulsive force through impact. John