Polarization propagator partitioned

Exercise 10.3 Derive the partitioned form of the matrix representation of the polarization propagator, Eq. (10.15), using the relation for the inverse of a blocked matrix, Eq. (10.14). 

Nielsen et al., 1980) all terms in the partitioned form of the polarization propagator, Eq. (10.15), are evaluated through second order. This implies that we have to include now also contributions from the fi2 operators, because the first nonvanishing term in the (Pa)(Af2..-2 - ) Af2...i or Afi2...(Af2...2 ) T2...(0. ..) and Mi2(M22) Af2i contributions is of second order, as discussed earlier and has to be included now. 

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