Problems QFT 4

1. Show that the Hamiltonian operator of the Dirac field is the integral of the number densities of particles and antiparticles times the energy.
2. Show that [math]\displaystyle{ \sum_s u^s(p)\bar u^s(p)=\gamma\cdot p +m }[/math].
3. What is the operator C that changes particles into antiparticles for a Dirac field?
4. Among the following interaction lagrangians [math]\displaystyle{ g\Phi(x)\bar\psi(x)\psi(x) }[/math], [math]\displaystyle{ g(\partial_\mu A^\mu)^4 }[/math], [math]\displaystyle{ g \Phi^3 }[/math], which ones are renormalisable in spacetimes of dimension 4 or 6 ?