1. Calculate the norm of a 1-particle state in the case of an inverted bosonic algebra $[a^\dagger,a]=1$.
2. In the case of a complex scalar field, show that the charge can be written $Q=\int\frac{d^3p}{(2\pi)^3}(a^\dagger_{\vec p} a_{\vec p}-b^\dagger_{\vec p} b_{\vec p})$.
3. For a massless particle, calculate the retarded propagator $[\Phi^*(x),\Phi(y)]$ in $x$ space.
4. Find the expression of the Dirac hamiltonian corresponding to the Dirac equation for 1-particles states. Show that it commutes with $\overrightarrow L+\overrightarrow{\Sigma\over 2}$ and $\overrightarrow p\cdot\overrightarrow\Sigma$.