# Using the Goldstone theorem

1. Dec 30, 2011

### ben133

1. The problem statement, all variables and given/known data
Consider a gauge theory with gauge group SU(3). Suppose that the matter field content consists of four different complex scalars, all transforming as triplets of SU(3). Suppose that the potential is the most general possible potential such that the only symmetry of the complete Lagrangian is the gauge SU(3).
On the basis of the Goldstone theorem, how many massive/massless real scalars are going to be present in the spectrum? How many massive/massless gauge bosons?

3. The attempt at a solution
I'm honestly at a loss here, I'm trying to revise for an exam, and this is a past paper problem. I know how to use the generalized Goldstone theorem if I know what the gauge symmetry is, and what it goes to. e.g. if if SO(3) -> SO(2) then there are 2 Goldstone bosons, but I don't know how to use the theorem in the case mentioned above. I assume the massless gauge bosons it asks for are the Goldstone bosons, and the massive ones would be 'normal' bosons, is this true?