I am reading the fantastic QED Feynman book. He talks in chapter 3 about a formula he considers too complicated to be written in the book. I would like to know which formula he talks about, although I have a vague idea. Please don't shy away from writing it properly, or giving a non-popular description or reference, I am conversant with basic QM, although not with the variational formulation nor QFT in general.
He talks about a formula for E(A to B), the amplitude for an electron to go from B to A in a space-time diagram), and states that it
(...)can be represented by a giant sum of a lot of different ways an electron could go from point A to point B in space-time. The electron could take a 'one-hop flight' going directly from A to B; it could take a 'two-hop flight', stopping at an intermediate point C; it could take a 'three-hop flight' (...) The amplitude for each 'stop' is represented by $n^2$ (...) The formula for E(A to B) is thus a series of therms (...) for all possible intermediate points
Additionally, I would like to know whether this book is another literal transcription of some lectures video footage, as it happens with, for instance, the 1964 Messenger Lectures at Cornell (published as The Pleasure of Finding Things Out). This is secondary and can be answered in a comment for instance, if you like it so.