(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Determine the mass of the scalars and show that one remains zero in accordance with goldstones theorem.

2. Relevant equations

$$L=\dfrac {1}{2} (\partial_\mu \phi_a)(\partial^\mu \phi_a)-\dfrac{1}{2} \mu^2 (\phi_a \phi_a) - \dfrac{1}{4} \lambda (\phi_a \phi_a)^2+ i\bar{\psi} \gamma^\mu \partial_\mu \psi -g\bar{\psi} (\phi_1 +i\gamma^5 \phi_2)\psi$$

I have chosen a vacuum solution that breaks the symmetry

$$\phi_1 = \sqrt{\dfrac{-\mu^2}{\lambda}}, \phi_2 =0$$

3. The attempt at a solution

So I know that I need to expand the fields around the minimum and then write the new lagrangian, then I should be able to read the mass from the hyperbolic terms, but I'm not sure how to carry out the expansion. Any advice would be much appreciated :)

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# Homework Help: Spontaneous symmetry breaking scalar field masses

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