# Coulomb Gauge vs. Lorentz Gauge transformation

1. May 8, 2009

### kthouz

Given a set of a scalar function V and a vector function, how does one recognize that it is a coulomb gauge or lorentz gauge transformation?
Actually there is a method that i use but i am not sure if it is always true:
what i do is to make an electric field (from that set and using known gauge transformation) and see if it has the form a coulomb electric field (static field). If it does i conclude that it is a coulomb gauge, else it is a Lorentz gauge.
Am i right?

2. May 8, 2009

### Staff: Mentor

You can find descriptions of the Coulomb and Lorentz gauge conditions here:

http://en.wikipedia.org/wiki/Gauge_fixing

(and probably in any E&M textbook at the intermediate level or above.)

If this isn't what you're looking for, please clarify...

Also note that there is in principle an infinite set of possible gauges, of which Coulomb and Lorentz are only two.

3. May 8, 2009

### dx

The Coulomb and Lorenz gauges are not gauge transformations. They are auxiliary conditions on the four-potential that we may choose because of the fact that there is gauge freedom. If you have a given four-potential Aµ, and you want to check if it satisfies the Lorenz gauge, all you have to do is show that ∂µAµ = 0.

4. Jun 12, 2011

Exactly. And how do you show this?
This is my question ....

5. Jun 12, 2011

Staff Emeritus
You take the derivative.