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.