Find the gauge transformation of a Lagrangian

[silverwhale]

Homework Statement

The lagrangian is given by:
$$L = -\frac{1}{4} F^2_{\mu \nu} + (\partial_{\mu} \phi_1 - m_1 A_{\mu})^2 + (\partial_{\mu} \phi_2 - m_2 A_{\mu})^2$$

Homework Equations

Find the gauge transformation of the fields that corresponds to a symmetry.
Find the combination of scalar fields which couples to A_mu.

The Attempt at a Solution

I am clueless here, any idea would be great.

 

[mark726]

Hello! It seems like you are working with a Lagrangian that describes a gauge theory. In order to find the gauge transformation of the fields, you can use the Noether's theorem. This theorem states that for every continuous symmetry, there exists a corresponding conserved current. In the case of gauge theories, the conserved current is related to the gauge transformation of the fields. So, you can start by identifying the continuous symmetry in your Lagrangian and then use the Noether's theorem to find the gauge transformation.

As for the combination of scalar fields that couples to A_mu, you can look at the terms in the Lagrangian that contain A_mu and see which scalar fields they are multiplied with. These scalar fields will be the ones that couple to A_mu. I hope this helps!