When I was an undergrad and graduate EE student, the "go to" book to help with electromagnetics was Div, Grad, Curl, and all that (http://www.amazon.com/Div-Grad-Curl-All-That/dp/0393925161). Back in my era it was the 1st edition of the book, not the 4th.

I see another book with good recommendations, A Student's Guide to Maxwell's Equations (http://www.amazon.com/Students-Guide-Maxwells-Equations/dp/0...) but I have not read that one.

Div, Grad, Curl helped a bit, but what really made it click for me was an excellent professor some other EE math-class-in-disguise that explained those vector calc operations in terms of divergence (source density) and flux (change in time/space).

As far as understanding the linked paper, I can't follow the proof either. Equations 1-4 I've never seen, 5-8 are Maxwell's Equations which are familiar but we wrote them with different notation, 9-18 are again equations I've never seen. The meat of the proof in 19-21 is built on 14 mystery equations and 4 that I recognize.

As a former EE I guess we didn't prove equations as much as take their existence as given and then figured out what that implied for the real world. ;) Other posters aroberge and wraithm have mentioned also needing QM from physics to follow the proof, which must be where the other equations are from!

Surely you have seen equation 1 (but perhaps with a slightly different notation). Each dot above an x represent a time derivative. So, the left-hand side is the second derivative of the position with respect to time aka the acceleration, times the mass. So, the first equation is simply F = ma (but, yeah... the notation can easily throw one off if one has not see it before.)

You're correct, I didn't recognize it. Thanks for pointing that out!

The proof starts from two sets of equations:

1. Newton's second law (first year undergraduate)

2. Commutation relations in QM (2nd or 3rd year undergraduate)

To make the desired connection, one must have seen Maxwell's Equations (which some first year undergraduate physics textbooks include).

There is no need to assume graduate level physics; someone having done a B.Sc. in Physics should know more than enough to follow this derivation.

Yeah my Political Science degree is not much help at the moment.