# Maxwell's equations from U(1) symmetry

## Main Question or Discussion Point

I understand that one is able to derive the inhomogenuous pair of Maxwell's equations from varying the field strength tensor Lagrangian.

Now implying the U(1) gauge invariance, how is one led to the Maxwell's equations?

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dextercioby
Homework Helper
I understand that one is able to derive the inhomogenuous pair of Maxwell's equations from varying the field strength tensor Lagrangian [...]
No, the homogenous pair results that way. To get the inhomogenous ones you need to add in a term for coupling to (charged) matter.

[...] Now implying the U(1) gauge invariance, how is one led to the Maxwell's equations?
From a geometric perspective, U(1) is embedded in the field.

From a geometric perspective, U(1) is embedded in the field.
Could you give me a few hints on how to do it explicitly or is this already enough to manage with the task of deriving the equations?

Thanks.

Alright so i reached the point where you get an interaction term in the lagrangian density leading to the inhomogenuous pair of Maxwell's equations.

But to me the intrudiction of a covariant derivative is a little confusing. It seems perfectly reasonable to require that physics stay the same under U(1) symmetry. But adding the vector potential and simply implying an ad hoc transformation rule seems unjustifiable. Also, why do we have to add the elementary charge and planks constant to it? Is this required from dimensional analysis?

And from the Wikipedia article i understand, that the homogenuous pair still only arises from the same old field tensor Lagrangian.

Can anyone clear it up for me?

Thanks.

Avodyne