Testing the master constraint programme for loop quantum gravity: V. Interacting field theories
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 nonAbelian 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 backgroundindependent quantum field theories such as loop quantum gravity (LQG) this might become possible by working in a new, backgroundindependent 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.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 February 2006
 DOI:
 10.1088/02649381/23/4/005
 arXiv:
 arXiv:grqc/0411142
 Bibcode:
 2006CQGra..23.1143D
 Keywords:

 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory;
 Mathematical Physics;
 Mathematics  Mathematical Physics
 EPrint:
 20 pages, no figures