Problems QFT 4 (Redirected from Exercices 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 ?