I am working though some questions for my QFT/ QED exam and i am having trouble with the following question:

Explain why the following terms cannot be part of the Langrangian of QED:

1. $-g(\bar{\psi}\psi)^2$
2. $\frac{1}{2}m^2A_\mu A^\mu$
3. $-\frac{1}{4}F_{\mu \nu}\Box F^{\mu \nu}$

My Answers:

1. I have no idea. An interaction term; it obeys the local U(1) invariance.
2. This would suggest that the photon has mass, which we know it doesnt have.
3. I don't know if there are more or better reasons but, I think this term cannot be present as it does not represents the actual Lagrangian of electromagnetism. This term would implement a distorted version of it.

Are my answers correct or are there better arguments

I am working though some questions for my QFT/ QED exam and i am having trouble with the following question:

Explain why the following terms cannot be part of the Lagrangian of QED:

1. $-g(\bar{\psi}\psi)^2$
2. $\frac{1}{2}m^2A_\mu A^\mu$
3. $-\frac{1}{4}F_{\mu \nu}\Box F^{\mu \nu}$

My Answers:

1. I have no idea. An interaction term; it obeys the local $U(1)$ invariance.

2. This would suggest that the photon has mass, which we know it doesnt have.

3. I don't know if there are more or better reasons but, I think this term cannot be present as it does not represents the actual Lagrangian of electromagnetism. This term would implement a distorted version of it.

Are my answers correct or are there better arguments?

I am working though some questions for my QFT/ QED exam and i am having trouble with the following question:

Explain why the following terms cannot be part of the Langrangian of QED:

1. $-g(\bar{\psi}\psi)^2$
2. $\frac{1}{2}m^2a_\mu a^\mu$
3. $-\frac{1}{4}f_{\mu \nu}\Box f^{\mu \nu}$

My Answers:

1. I have no idea. An interaction term; it obeys the local U(1) invariance.
2. This would suggest that the photon has mass, which we know it doesnt have.
3. I don't know if there are more or better reasons but, I think this term cannot be present as it does not represents the actual Lagrangian of electromagnetism. This term would implement a distorted version of it.

Are my answers correct or are there better arguments

I am working though some questions for my QFT/ QED exam and i am having trouble with the following question:

Explain why the following terms cannot be part of the Langrangian of QED:

1. $-g(\bar{\psi}\psi)^2$
2. $\frac{1}{2}m^2A_\mu A^\mu$
3. $-\frac{1}{4}F_{\mu \nu}\Box F^{\mu \nu}$

My Answers:

1. I have no idea. An interaction term; it obeys the local U(1) invariance.
2. This would suggest that the photon has mass, which we know it doesnt have.
3. I don't know if there are more or better reasons but, I think this term cannot be present as it does not represents the actual Lagrangian of electromagnetism. This term would implement a distorted version of it.

Are my answers correct or are there better arguments