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  Testing the Master Constraint Programme for Loop Quantum Gravity V. Interacting Field Theories

Dittrich, B., & Thiemann, T. (2006). Testing the Master Constraint Programme for Loop Quantum Gravity V. Interacting Field Theories. Classical and Quantum Gravity, 23(4), 1143-1162.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-4AF6-2 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-4AF7-F
Genre: Journal Article

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0411142.pdf (Preprint), 274KB
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 Creators:
Dittrich, Bianca1, Author              
Thiemann, Thomas1, Author              
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1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:24014              

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 Abstract: This is the fifth and final paper in our series of five in which we test the master constraint programme for solving the Hamiltonian constraint in loop quantum gravity. Here we consider interacting quantum field theories, specifically we consider the non-Abelian Gauss constraints of Einstein–Yang–Mills theory and 2 + 1 gravity. Interestingly, while Yang–Mills theory in 4D is not yet rigorously defined as an ordinary (Wightman) quantum field theory on Minkowski space, in background-independent quantum field theories such as loop quantum gravity (LQG) this might become possible by working in a new, background-independent representation. While for the Gauss constraint the master constraint can be solved explicitly, for the 2 + 1 theory we are only able to rigorously define the master constraint operator. We show that the, by other methods known, physical Hilbert is contained in the kernel of the master constraint, however, to systematically derive it by only using spectral methods is as complicated as for 3 + 1 gravity and we therefore leave the complete analysis for 3 + 1 gravity.

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Language(s): eng - English
 Dates: 2006
 Publication Status: Published in print
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 Identifiers: eDoc: 205894
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Title: Classical and Quantum Gravity
Source Genre: Journal
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Pages: - Volume / Issue: 23 (4) Sequence Number: - Start / End Page: 1143 - 1162 Identifier: -