[Physics] The path integral and Feynman diagrams

Question

This question is somewhat of a historical one, but it also contains some physics. I am curious to find how exactly the concept of Feynman diagrams arose (I assume from Feynman's path integral)?

The leap from path integrals to diagrammatic computations isn't obvious (to me, at least); I'd like to understand better how Feynman's thinking approximately developed. For instance, how did he come up with interpreting the propagator as the propagation of particles? Was there a particular analogy that can be made? Is there any understanding to be gained by learning how the technique was originally developed?

I realize that my phrasing might be a quite vague. If the question is too broad as of right now, please let me know how I can improve on it!

Answer 1

For instance, how did he come up with interpreting the propagator as the propagation of particles?

The path integral is usually introduced as a matrix element of the time evolution operator $$ \langle x_f\lvert\mathrm e^{-\frac{\mathrm i}{\hbar}\hat{H}(t_f-t_i)}\lvert x_i\rangle, $$ which is a measure of the probability of finding a system in final state and time $x_f,t_f$ when it had been in state $x_i$ at time $t_i$ initially. It is quite plausible to name it propagator as it gives immediate access to the probability that a system, maybe only a single particle, propagates from state $x_i$ to $x_f$ in time $t_f-t_i$. Probably it is more difficult to understand that this notion is still maintained when the path integral is used to calculate the grand partition sum in quantum statistics.

Is there any understanding to be gained by learning how the technique was originally developed?

The idea of symbolizing formulae by nodes and connections between them is used in many other fields and was probably not new at the time. The idea is basically that of an isomorphism between a class of graphs and, given an unambiguous translation rule, the formulae at hand. This gives intuitive connection to graph theory and eases its application, for instance when a diagram is called 'connected' or 'disconnected', meaning that the respective formula can be factorized or not. Another example of this kind that is not related to Feynman is the diagrammatic treatment of the classical Ising model.