Maxwell Equations: Deriving 1 Equation from 2

[ghery]

Hi:

In electromagnetism, Maxwell equations originally were 6, with the aid of vector analysis, these equations were simplified and they became 4, after that with the aid of special relativity and tensor analysis (for the electromagnetic tensor) they became 2.

Now I have seen (I don't remember where) that these two equations became just one without any loss of information, Does anybody know how to derive these equation?, What is that equation?, and by the way what other mathematical tools do I need in order to derive it?

Thanks for your support

 

[ismaili]

Hi:

In electromagnetism, Maxwell equations originally were 6, with the aid of vector analysis, these equations were simplified and they became 4, after that with the aid of special relativity and tensor analysis (for the electromagnetic tensor) they became 2.

Now I have seen (I don't remember where) that these two equations became just one without any loss of information, Does anybody know how to derive these equation?, What is that equation?, and by the way what other mathematical tools do I need in order to derive it?

Thanks for your support

I guess what you want is Maxwell equations written in terms of differential forms. However, it takes two. You may first try
http://en.wikipedia.org/wiki/Maxwell's_equations
As for the basic introduction of forms, you can read Ryder's QFT book.