# Quantum Field Theory-Mass spectrum of Lagrangian

Tags:
1. Jan 9, 2019

### jgarrel

1. The problem statement, all variables and given/known data
We are given the Lagrangian density:
$$\mathcal{L}=\partial^\mu \phi ^* \partial_\mu \phi - m\phi^* \phi +\sum_{\alpha =1} ^2 ( \overline{\psi}^\alpha (i\gamma^\mu \partial_\mu -m)\psi^\alpha -g\overline{\psi}^\alpha\psi^\alpha \phi^* \phi)$$
, where $\phi$ is a complex scalar field, $\psi ^1$ $\psi ^2$ are Dirac fields and m,g are constants.

We are asked to find the mass and the spin of the particles that this theory describes.
2. Relevant equations

3. The attempt at a solution
I thouht about using spontaneous symmetry breaking and the Higgs mechanism, but I don't know how to deal with the kind of coupling presented in this problem.