## September 2, 2006

### The Master constraint program in LQG

#### Posted by Aaron

I’m a little reluctant to post much on the master constraint program because I haven’t read much on it. But I thought I’d post this if others want to comment on the subject.

My initial question is how does the master constraint program work in classical mechanics? In particular, say we are given some symplectic manifold and some set of constraints. The master constraint is$$M={K}^{\mathrm{IJ}}{C}_{I}{C}_{J}.$$Using this, how does one obtain the constrained phase space?

Or is this the wrong question to ask?

### The Harmonic Oscillator in LQG

#### Posted by Aaron

I’ve been trying to understand Thomas Thiemann’s riposte to the papers of Nicolai, Peeters and Zamaklar, Nicolai and Peeters and Helling and Policastro. I’m fairly busy right now with a paper of my own and moving, so I’ll concentrate on the part where he describes how LQG-quantization replicates the usual quantization of the harmonic oscillator. Maybe later, I can get to trying to understand the master constraint program.

I’ve already posted some comments at Christine Dantas’s blog, but I thought I might also try to post them here. I really would love to see some sort of discussion on these points. One of the things I think any scientist should be able to do is to get in front of a chalkboard and be able to communicate a pretty good idea about what’s going on with their work. Think of this as a long distance chalkboard, and I’m the skeptical visitor.

Anyways, I will try in this post to summarize my understanding of the construction in Thiemann. I hope people will correct me if I get it wrong. (And I hope I get the algebra correct….)