/sci/ - Science & Math

This isnt a homework thread, this is a fucking physics thread about a consent i don't understand, go ban the fucking retarded non-science threads first if you want to excersice your power as a mod.

im studying gauge invariance and im not sure about the details of the flowing derivation:

Define a scalar quantity U(y,x) that transform as follows:
<div class="math"> U\left(y,x\right) \to e^{i \alpha \left(y\right)}U \left(y,x\right)e^{-i \alpha \left(x\right)}</div>
in general U = <span class="math"> e^{i\phi(y,x)}[/spoiler] for some phi and for an infinitesimal transformation we have:
<div class="math"> U(x+\epsilon n,x) = 1-ie \epsilon n^\mu A_\mu (x) </div>
where e is some constant.

now the book says the following:
inserting <span class="math"> U(x+\epsilon n,x) = 1-ie \epsilon n^\mu A_\mu (x) [/spoiler] into <span class="math"> U\left(y,x\right) \to e^{i \alpha \left(y\right)}U \left(y,x\right)e^{-i \alpha \left(x\right)}[/spoiler] shows that <span class="math"> A_\mu[/spoiler] transforms as
<div class="math"> A_\mu(x) \to A_\mu(x) - \frac{1}{e}\partial_\mu \alpha(x) </div>
i dont get this last part. how do you get the transformation law of <span class="math"> A_\mu[/spoiler] ?