I got a nice present today which included one of Feynman’s QED books. I noticed some early mistakes, and since I can’t find an errata page anywhere, I’ll collect them here.
Page 6 typos.
The electric field is given in terms of only the scalar potential
and should be
The invariant gauge transformation for the vector and scalar potentials are given as
But these should be
The sign was crossed on the scalar potential transformation. Feynman is also probably used to using , but he doesn’t do that explicitly at a different point on the page, so including it here is proper.
Page 7 notes.
The units in the transformation for the wave function don’t look right. We want to transform the Pauli equation
with a transformation of the form
Where is presumed, and we want to find the proportionality constant required for invariance. With we have
For the time partial we have
and the scalar potential term transforms as
Putting the pieces together we have
We need one more intermediate result, that of
So we have
To get rid of the , and time partials we need
This also kills off all the additional undesirable terms in the transformed operator (with ), leaving the invariant transformation completely specified
This is a fair bit different than Feynman’s result, but since he starts with the wrong electrodynamic guage transformation, that’s not too unexpected.
This isn’t errata, but I found the following required slight exploration. He gives (implicitly)
Is this an average over space and time? How would one do that? What do we get just integrating this over the volume? That dot product is . Our average over the volume, for , using wolfram alpha to do the dirty work
Since the sine integral vanishes, we have just as expected regardless of the angular frequency . Okay, that makes sense now. Looks like is only relavent for the single Fourier component, but that likely doesn’t matter since I seem to recall that the fourier component of this oscillators in a box problem was entirely constant (and perhaps zero?).