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Problems QFT 4

From IFPA wiki
  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]\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]g\Phi(x)\bar\psi(x)\psi(x)[/math], [math]g(\partial_\mu A^\mu)^4[/math], [math]g \Phi^3[/math], which ones are renormalisable in spacetimes of dimension 4 or 6 ?

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