Master constraint operators in loop quantum gravity

We introduce a master constraint operator (M) over cap densely defined in the diffeomorphism invariant Hilbert space in loop quantum gravity, which corresponds classically to the master constraint in the programme. It is shown that (M) over cap is positive and symmetric, and hence has its Friedrichs self-adjoint extension. The same conclusion is tenable for an alternative master operator (M) over cap', whose quadratic form coincides with the one proposed by Thiemann. So the master constraint programme for loop quantum gravity can be carried out in principle by employing either of the two operators. (c) 2006 Elsevier B.V. All rights reserved.