# Dirac's magnetic charge generalization of maxwell's equations?

1. Jun 3, 2008

### Peeter

I've seen two references to magnetic charge density as something that Dirac said would explain charge quantization. The first is in Schwartz's "Principles of Electrodyanamics" (Dover) where the author comments how it is unaesthetic that the two maxwell's equations aren't symmetric in form:

$$\partial_{\mu}F_{\mu\nu} = -4\pi j_v$$

$$\partial_{\mu}G_{\mu\nu} = 0$$

This book (1972), gives the idea mention, saying it would be nice to be able to write the second tensor equation as:

$$\partial_{\mu}G_{\mu\nu} = 4 \pi j_{\nu}^{(m)}$$

but procedes without it after such a mention "since no monopoles have as yet been seen".

Another reference was in:

http://www.plasma.uu.se/CED/Book/

This is an online book "Electromagnetic field theory", by Bo Thide where it's given more than just a passing reference. However, reading this I'm unclear whether it's just a theoretical idea. Is there now experimental data that the Dirac symmetrized Maxwells' equations explains (perhaps more than just the monopole idea) that the standard form doesn't?

In more advanced (quantum electrodynamics?) or more modern treatments of electrodynamics does this idea have any place?

2. Jun 5, 2008

### Creator

Not farmiliar with the eqns., but I thought Dirac condition for the magnetic monopole doesn't symmetrize the charges but only quantizes,the Dirac condition being ....

eg = hc/4pi ....where g = magnetic charge

Creator

3. Jun 6, 2008

### Peeter

The equations I was referring to are: 1.50a-d from EMFT_Book.pdf here:

http://www.plasma.uu.se/CED/Book/EMFT_Book.pdf

$$\nabla \cdot E = \rho^e/\epsilon_0$$

$$\nabla \times E = -\frac{\partial B}{\partial t} - \mu_0 j^m$$

$$\nabla \cdot B = \mu_0 \rho^m$$

$$\nabla \times B = \epsilon_0 \mu_0 \frac{\partial E}{\partial t} + \mu_0 j^e$$