Why would I want to fix a gauge?

[hideelo]

If I have a theory withsome gauge symmetry, I don't understand why we want to fix a gauge. It seems to me to be
1. artificial
2. ignoring a real symmetry of the equations

For example in electromagnetism, we can use the lorentz gauge, but why would I? It removes a degree of freedom that should be there and in its place puts in a constraint that has no basis in the physics of the system.

Edit: to emphasize this, if we choose the Lorentz gauge, aren't we throwing out all cases that don't satisfy that constraint? What happens to those cases?

 

[Orodruin]

The entire point of gauge theory is that your result does not depend on the gauge you select. Thus, you can pick any gauge and do your computations in that gauge. If you do not, you will be left with quantities (such as the vector potential) which are determined only up to arbitrary gauge transformations. You are only removing degrees of freedom which are not physical.

Edit: If you want to be a bit more stringent about it. Gauge theory is a theory of equivalence classes of gauge potentials, the equivalence being that potentials resulting in the same physical observables are equivalent. You can pick any representative from the equivalence class and do the computations with it.

 

[Dale]

I don't understand why we want to fix a gauge.

To simplify computations.

It removes a degree of freedom that should be there

The degree of freedom that is removed is not a physical degree of freedom.

 

[cosmik debris]

...Lorenz not the other guy.

 

[hideelo]

...Lorenz not the other guy.

You are right, I stand corrected