Quantum Spin Dynamics VIII. The Master Constraint

Details Quantum Spin Dynamics VIII. The Master Constraint Quantum Spin Dynamics VIII. The Master Constraint

2005-10-04

arxiv.org/abs/gr-qc/0510011v1

Class.Quant.Grav. 23 (2006) 2249-2266

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

19p, no figures

Scientific paper

Recently the Master Constraint Programme (MCP) for Loop Quantum Gravity (LQG) was launched which replaces the infinite number of Hamiltonian constraints by a single Master constraint. The MCP is designed to overcome the complications associated with the non -- Lie -- algebra structure of the Dirac algebra of Hamiltonian constraints and was successfully tested in various field theory models. For the case of 3+1 gravity itself, so far only a positive quadratic form for the Master Constraint Operator was derived. In this paper we close this gap and prove that the quadratic form is closable and thus stems from a unique self -- adjoint Master Constraint Operator. The proof rests on a simple feature of the general pattern according to which Hamiltonian constraints in LQG are constructed and thus extends to arbitrary matter coupling and holds for any metric signature. With this result the existence of a physical Hilbert space for LQG is established by standard spectral analysis.

Affiliated with

Also associated with

No associations

Rating

Quantum Spin Dynamics VIII. The Master Constraint does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Quantum Spin Dynamics VIII. The Master Constraint, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantum Spin Dynamics VIII. The Master Constraint will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-83214