R5

1. What would be the relation between [math]\displaystyle{ M_W }[/math] et [math]\displaystyle{ M_Z }[/math] if one broke [math]\displaystyle{ SU(2)\otimes U(1) }[/math] via a triplet ?
2. What are the gauge boson masses if one breaks [math]\displaystyle{ SU(3) }[/math] through a Higgs field in the fundamental representation ?
3. Diagonalize [math]\displaystyle{ \left( \begin{array}{cc} i & 2 \\ 1 & i \end{array} \right) }[/math] via two unitary transforms.
4. Consider several possible parametrisations of the CKM matrix, and show that the phase is not uniquely positioned in the matrix.
5. Calculate [math]\displaystyle{ \int d^2 PS }[/math] and [math]\displaystyle{ \int d^2 PS(p,k)\ p^\alpha k^\beta }[/math] for massless particles.