Quantum spin dynamics: VIII. The master constraint

Thiemann T (2006)

Publication Status: Published

Publication Type: Journal article

Publication year: 2006



Book Volume: 23

Pages Range: 2249-2265

Journal Issue: 7

DOI: 10.1088/0264-9381/23/7/003


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.

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Thiemann, T. (2006). Quantum spin dynamics: VIII. The master constraint. Classical and Quantum Gravity, 23(7), 2249-2265. https://dx.doi.org/10.1088/0264-9381/23/7/003


Thiemann, Thomas. "Quantum spin dynamics: VIII. The master constraint." Classical and Quantum Gravity 23.7 (2006): 2249-2265.

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