Master Constraint Operator in Loop Quantum Gravity

We introduce a Master Constraint Operator M̂ densely defined in the diffeomorphism invariant Hilbert space in loop quantum gravity. The corresponding quadratic form coincides with the one proposed by Thiemann in the master constraint programme. It is shown that M̂ is positive and symmetric, and hence has its Friedrichs self-adjoint extension. So the master constraint programme for loop quantum gravity can be carried out in principle by employing M̂.