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## Homework Statement

I need to gauge the symmetry:

[tex]

\phi \rightarrow \phi + a(x)

[/tex]

for the Lagrangian:

[tex]

L=\partial_\mu\phi\partial^\mu\phi

[/tex]

## Homework Equations

## The Attempt at a Solution

We did this in class for the Dirac equation with a phase transformation and I understood the method, but can't seem to figure out a way to apply the same approach to this field. All I have done so far is plug the transformation into the Lagrangian, but what I'm not sure about is what form the gauge field [tex]A_\mu[/tex] needs to take, or even where in the Lagrangian to put it! I have a load of QFT books too but the only mention of gauge invariance in them is very brief, not at all comprehensive, and is way further into the book than I am currently. Any guidance on where to start or where to read further would be really appreciated. Thanks as always!