Exam questions on renormalisation

1. How is mass renormalised in the [math]\displaystyle{ \lambda\Phi^3 }[/math] theory? What happens if the theory is non-renormalisable? Give an explicit example.
2. How can one calculate the imaginary part of a loop? Give one example.
3. Calculate the one-loop correction to the photon propagator. What does it imply for the coupling constant.
4. Consider the one-loop correction to the electron propagator. How many divergences does it contain? How can the theory be redefined to avoid these?
5. What is the renormalisation group and how does one choose scales in an RG-improved calculation?