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

TL;DR

This paper evaluates the Master Constraint Programme in Loop Quantum Gravity by applying it to interacting field theories like Einstein-Yang-Mills and 2+1 gravity, exploring its potential for background independent quantum field theories.

Contribution

It extends the Master Constraint Programme to interacting theories, including non-Abelian constraints, in a background independent setting, advancing the approach's applicability.

Findings

Successful application to Einstein-Yang-Mills constraints

Analysis of 2+1 gravity within the framework

Insights into background independent quantum field theories

Abstract

This is the final fifth 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, specificlly we consider the non -- Abelean 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.