Testing the Master Constraint Programme for Loop Quantum Gravity IV. Free Field Theories

TL;DR

This paper extends the Master Constraint Programme to free field theories like Maxwell and linearized gravity in Loop Quantum Gravity, addressing technical challenges in handling constraint operator distributions.

Contribution

It demonstrates how to apply the Master Constraint Programme to free field theories, highlighting necessary methodological adaptations for operator distribution issues.

Findings

Successful formulation of the Master Constraint for Maxwell and linearized gravity

Identification of key technical considerations in constraint operator squares

Framework for future applications to more complex theories

Abstract

This is the fourth paper in our series of five in which we test the Master Constraint Programme for solving the Hamiltonian constraint in Loop Quantum Gravity. We now move on to free field theories with constraints, namely Maxwell theory and linearized gravity. Since the Master constraint involves squares of constraint operator valued distributions, one has to be very careful in doing that and we will see that the full flexibility of the Master Constraint Programme must be exploited in order to arrive at sensible results.