Finite-dimensional Feynman Diagrams

Feynman diagrams are a fundamental tool for the investigation and explanation of phenomena in quantum field theory. Their origin, however, is purely mathematical: they give a convenient way of organizing and encoding certain important calculations.

In this column we will look at a finite-dimensional calculation that shares many of the formal properties of the calculation of interest.

The mathematics involved is more technical than usual in this series of columns, but it is quite concrete. With the restriction to finite-dimensionality we will see exactly where the ``diagrams'' come into the picture, using no more than fairly elementary procedures from calculus and linear algebra. So any third or fourth-year undergraduate should be able to follow the details, while a broader audience should be able to gain from the examples an accurate picture of the whole procedure.