R2b

1. Consider [math]\displaystyle{ SU(2)\otimes U(1) }[/math] breaking by a scalar field with a v.e.v. (v,0) instead of (0,v). What are the consequences?
2. Let [math]\displaystyle{ \phi_1 }[/math] and [math]\displaystyle{ \phi_2 }[/math] be two scalar fields. One defines [math]\displaystyle{ \chi_1=(c\phi_1+s\phi_2) }[/math] as a new field. What will the algebra be for its creation and annihilation operators? Same question for fermions.
3. Show that the SU(3) breakings mentioned in lecture lead to gauge boson masses [math]\displaystyle{ 3gv^2\ (SU(3)\to SU(2)\otimes U(1)) }[/math] or [math]\displaystyle{ \sqrt{2g} v }[/math] and [math]\displaystyle{ \sqrt{g} v \ (SU(3)\to U(1)\otimes U(1)). }[/math])