# Feynman diagrams for phi phi -> phi phi

1. Oct 31, 2015

### silverwhale

1. The problem statement, all variables and given/known data
Compute the matrix element for the scattering process $$\phi \phi \to \phi \phi$$

2. Relevant equations
The Lagrangian is given by
$$L = \frac{1}{2} \partial_{\mu} \phi \partial^{\mu} \phi + \frac{\alpha}{2} \phi \partial_{\mu} \phi \partial^{\mu} \phi + \frac{\beta}{2} \phi^2 \partial_{\mu} \phi \partial^{\mu} \phi$$

3. The attempt at a solution
At tree level I included a 4 legged vertex diagram + 3 diagrams with an internal line. Is this correct? I get a delta function with 4 momenta ( multiplied with other terms) + product of 2 delta functions with 3 momenta (multiplied with other terms) equal to the scattering implitude multipplied by a delta function of 4 momenta.

Now my question is just what are the Feynman diagrams for the general process: $$\phi \phi \to \phi \phi$$

2. Oct 31, 2015

### silverwhale

If we consider an other case where the interaction term looks like $$c_1 \phi^3 + c_2 \phi^4,$$ can one just sum up the feynman diagrams (for eg. tree level diagrams) for phi3 theory and phi4 theory to express the $$\phi \phi \to \phi \phi$$ scattering?