# Gauge invariance and it's relation to gauge bosons

Hello,
I'm currently doing a project that is concerned with the hopeful discovery of the Higgs Boson at LHC. I'll be running some code that my supervisor has produced, but before that he wanted me to understand more of the physics that is behind the Higgs mechanism.

He has proposed a question to me, "Why gauge invariance forbids mass terms for gauge bosons?"

I've been reading quite a few textbooks and i'm not too sure if this could be the answer to the problem. The answer had an explanation from the Bose-Einstein condensate (BEC) context, where it talks about definite phase of the complex wavefunction describing the BEC and the existence of such a phase breaks global gauge invariance - a symmetry associated with particle conservation.
Could this particle conservation be the reason for no mass terms in gauge invariance? Another possible answer could be a chapter I read on about the Goldstone boson.

I have a feeling that the two possible explanations that i've provided for the question are way off the mark.

Could anyone recommend a textbook, particular topics about the question or websites that may shed some light on my question?

Cheers.

"Why gauge invariance forbids mass terms for gauge bosons?"

fermion mass terms in the lagrangian $$m\bar{\psi}\psi$$ are scalar. Maybe you should try to rewrite this term as a function of $$\psi_L$$ and $$\psi_R$$ ?

The reason why a by-hand mass term is forbidden in a gauge theory is that this spoils gauge invariance and the theory loses renormalizability. These are two fundamental ingredients for the proper working of the theory. This difficulty can be evaded through the Higgs mechanism. The proof that a gauge theory with the Higgs mechanism is renormalizable is due to Veltman and 't Hooft as I think you know.

Cheers

Jon

"Why gauge invariance forbids mass terms for gauge bosons?"
Read chapers: 54, 58 and 69. of this book -> http://www.physics.ucsb.edu/~mark/ms-qft-DRAFT.pdf
In chapters 58 and 69 it is explicitly stated that theory with mass term in Lagrangian don't forbid gauge invariance!

Page 346 below equation 58.7

okey, you're right it's my mistake. His question was about mass term for gauge bosons not matter fields.