Editing Loop quantum gravity (section)

=== Algebraic quantum gravity (AQG) ===
The master constraint programme has evolved into a fully combinatorial treatment of gravity known as algebraic quantum gravity (AQG).{{sfn|Giesel|Thiemann|2007a|pp=2465–2498}} The non-graph changing master constraint operator is adapted in the framework of algebraic quantum gravity. While AQG is inspired by LQG, it differs drastically from it because in AQG there is fundamentally no topology or differential structure – it is background independent in a more generalized sense and could possibly have something to say about topology change. In this new formulation of quantum gravity AQG semiclassical states always control the fluctuations of all present degrees of freedom. This makes the AQG semiclassical analysis superior over that of LQG, and progress has been made in establishing it has the correct semiclassical limit and providing contact with familiar low energy physics.{{sfn|Giesel|Thiemann|2007b|pp=2499–2564}}{{sfn|Giesel|Thiemann|2007c|pp=2565–2588}}