Testing the master constraint programme for loop quantum gravity: V. Interacting field theories

Journal article


Publication Details

Author(s): Dittrich B, Thiemann T
Journal: Classical and Quantum Gravity
Publisher: IOP PUBLISHING LTD
Publication year: 2006
Volume: 23
Journal issue: 4
Pages range: 1143-1162
ISSN: 0264-9381


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 ail ordinary (Wightman) quantum field theory oil 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.



FAU Authors / FAU Editors

Thiemann, Thomas Prof. Dr.
Lehrstuhl für Theoretische Physik


How to cite

APA:
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. https://dx.doi.org/10.1088/0264-9381/23/4/005

MLA:
Dittrich, Bianca, and Thomas Thiemann. "Testing the master constraint programme for loop quantum gravity: V. Interacting field theories." Classical and Quantum Gravity 23.4 (2006): 1143-1162.

BibTeX: 

Last updated on 2018-10-08 at 19:54