# Daily Archives: July 27, 2007

## Feynman Diagrams for the Masses (part 2)

In part 1, we briefly discussed how Feynman diagrams show up in QFT with an example taken from QED (quantum electrodynamics). The calculation for the first order correction to the photon propagator (i.e. vacuum polarization) turned out to be a rather messy integral:

QFT’s little Infinity Problem

This is a mess because it (a) involves the trace of a product of four 4×4 matrices, (b) requires eight definite integrals, each from $\int_{-\infty}^{+\infty}$, and (c) gives infinity. Of these problems, the worst was the fact that the calculation gives infinity. This would make one conclude that the theory was nonsense, but there were some other calculations that worked, and what’s more important, the results of certain calculations could be evaluated as $(+\infty) + (-\infty) + k$ and k was a number which gave an excellent match to experiment.