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  Quantum Spin Dynamics VIII. The Master Constraint

Thiemann, T. (2006). Quantum Spin Dynamics VIII. The Master Constraint. Classical and Quantum Gravity, 23(7), 2249-2265.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-4B4E-7 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-4B4F-5
Genre: Journal Article

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cqg6_7_003.pdf (Publisher version), 216KB
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 Creators:
Thiemann, Thomas1, Author              
Affiliations:
1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014              

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 Abstract: 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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Language(s): eng - English
 Dates: 2006
 Publication Status: Published in print
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 Identifiers: eDoc: 241769
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Title: Classical and Quantum Gravity
Source Genre: Journal
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Pages: - Volume / Issue: 23 (7) Sequence Number: - Start / End Page: 2249 - 2265 Identifier: -