Testing the Master Constraint Programme for Loop Quantum Gravity II. Finite Dimensional Systems

TL;DR

This paper tests the Master Constraint Programme in Loop Quantum Gravity using simple finite-dimensional models with various constraints to evaluate its effectiveness in solving the Hamiltonian constraint.

Contribution

It introduces a systematic analysis of the Master Constraint Programme applied to finite-dimensional models with different types of constraints, advancing the understanding of its applicability.

Findings

Demonstrates the effectiveness of the Master Constraint Programme in simple models

Shows compatibility with both Abelian and non-Abelian constraints

Provides groundwork for applying the method to more complex systems

Abstract

This is the second paper in our series of five in which we test the Master Constraint Programme for solving the Hamiltonian constraint in Loop Quantum Gravity. In this work we begin with the simplest examples: Finite dimensional models with a finite number of first or second class constraints, Abelean or non -- Abelean, with or without structure functions.