  This is the fourth paper in our series of five in which we test the Master
Constraint Programme for solving the Hamiltonian constraint in Loop Quantum
Gravity. We now move on to free field theories with constraints, namely Maxwell
theory and linearized gravity. Since the Master constraint involves squares of
constraint operator valued distributions, one has to be very careful in doing
that and we will see that the full flexibility of the Master Constraint
Programme must be exploited in order to arrive at sensible results.
