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Problems QFT 6

From IFPA wiki
  1. Calculate directly the cross section for [math]\gamma\gamma\rightarrow e^+ e^-[/math] in the non polarised case in the ultrarelativistic limit [math]m_e \ll \sqrt{s} [/math].
  2. Calculate the cross section for [math]e^+ e^-\rightarrow\gamma\gamma [/math] in the non polarised case in the nonrelativistic limit [math]2 m_e\approx \sqrt{s}[/math].
  3. Gauge invariance tells us that [math] A_\mu[/math] and [math]A_\mu+\partial_\mu\Lambda[/math] give equal results. In [math]k[/math] space, this means that the polarisation vector of a photon of momentum [math]k_\mu[/math], [math]\epsilon_\mu[/math], and [math]\epsilon_\mu+c k_\mu[/math] give identical results. Show that this is the case for the Compton scattering amplitude.
  4. Imagine that the photon is a massless scalar [math]\phi[/math] that interacts with electrons via [math]{\mathcal L}_{int}=g\bar\psi\psi\phi[/math]. How would that affect the Compton cross section?



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