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# Motivation.

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.

# Third Lecture

## 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

so

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

Or

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.

# Second Lecture

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?).