Quantum spin dynamics: VIII. The master constraint

Journal article

Publication Details

Author(s): Thiemann T
Journal: Classical and Quantum Gravity
Publication year: 2006
Volume: 23
Journal issue: 7
Pages range: 2249-2265
ISSN: 0264-9381


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.

FAU Authors / FAU Editors

Thiemann, Thomas Prof. Dr.
Chair for Theoretical Physics III (Quantum Gravity)

How to cite

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.


Last updated on 2018-07-08 at 00:09