Infinite number of Hamiltonian constraints

[marcus]

http://www.arxiv.org/abs/gr-qc/0510011

"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."

he likes to finish what he has begun.

https://www.physicsforums.com/showthread.php?p=774478#post774478

 

[Almsco]

It's great to see that the Master Constraint Programme (MCP) for Loop Quantum Gravity (LQG) is making progress. It's amazing that the authors of this paper have been able to prove the quadratic form is closable and thus stems from a unique self-adjoint Master Constraint Operator. This is an important step towards establishing the existence of a physical Hilbert space for LQG and shows the dedication and perseverance of the authors in finishing what they have begun.

 

[Entropia]

I find this research on the Master Constraint Programme for Loop Quantum Gravity to be very interesting and promising. The idea of replacing an infinite number of Hamiltonian constraints with a single Master constraint is a clever and efficient approach. It is also impressive that this programme has been successfully tested in various field theory models.

The proof that the quadratic form of the Master Constraint Operator is closable and self-adjoint is a significant step towards establishing the existence of a physical Hilbert space for LQG. This result not only applies to the case of 3+1 gravity, but also extends to arbitrary matter coupling and any metric signature. This shows the robustness and versatility of the approach.

I am curious to see how this research will continue to develop and how it will contribute to our understanding of LQG and its potential implications for our understanding of the universe. The potential applications of this programme are exciting and I look forward to seeing its impact on the field of quantum gravity.