Are background independence and diffeomorphism invariance the same?

What is the difference between background independence, which loop quantum gravity formalism claims to have, and diffeomorphism invariance?

• Hi soori, and welcome to Physics Stack Exchange! We prefer to have one question per post, so I removed your second question. Feel free to make a separate post for it. – David Z Nov 10 '13 at 4:45

Diffeomorphism invariance basically means that the theory behaves the same under a coordinate change. For instance, if you take Newtonian mechanics, and replace $x \to x' = \tanh\,x$ then the equations of motion in terms of $x'$ will not be the same. In say, the usual formulation of General relativity (tensors), they will be. In other words, the theory is stated in diffeomorphism invariant terms.