The book is about Quantum ElectroDynamics, QED for short, a theory Feynman himself has contributed a lot to. It is a quantum description of the electromagnetic field, and how it interacts with matters carrying electric charge.
Feynman attempted to give an intuitive picture to everything he talked about. His usual style. And he is largely successful, although sometimes pictures he painted, while being technically correct, are very far from how people actually deal with the problem.
With one exception, though.
Near the end of the book, he described some then unsolved mysteries surrounding QED. Back then one of the biggest problems bugging physicists for years was those annoying infinities you get for virtually any calculation in QED.
Sure, there are ways ("renormalization", we call it) to get rid of these infinities -- but back then it wasn't so clear to physicists if this renormalization procedure is legitimate at all.
(There is a cartoon, still to be seen on the wall somewhere in every particle theory group's office space, making fun of how people "sweep all the infinities under the rug".)
Feynman of course wrote about this issue in the book, and said that the need of renormalization signifies something's not right.
Well, the general view on this issue changed during the '70s; the meaning of renormalization was re-interpreted by Kenneth Wilson. It is not to be thought of as just an exercise to remove "unphysical" infinities. But rather we admit that our theory is incomplete; it is going to fail when we push it to the extreme short-distance limit. The infinities signal the failure of the theory, and before we know what lies beyond (which we still don't), the sensible thing to do is to cut away this extreme limit.
Can't foul Feynman for not knowing the future development when he wrote the book. But just want to point out that his take on this issue is somewhat outdated....Continua