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Problems QFT 3

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

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