Effective Field Theory for Quantum Gravity from ... - Relativity Group

Relation of Dirac ObservablesIntersecting constraint surfaces in local coordinatesχ α = M β αq β ≈ 0 and σ β = N β α(p α − p α o ) with M β α and N β α intertibleequiv. doubly Abelian set: ˜χ α = q α ≈ 0 and ˜σ β = p β − p β o⇒ vector fields {˜χ α , .} and {˜σ β , .} are Frobenius integrable⇒ for every function f red on intersection Γ red there exists a local functionf on U ⊂ Γ s.t. {˜χ α , f } = 0 = {˜σ β , f } (doubly strong observables)⇒ for these preferred representatives the identification on full Γ is trivialf A ≡ f B .Abelianization generally spoils locality:Nonabelian case: there is still a dictionary for observables through the twophase space reductions of the linking theory.T. Koslowski (PI) Quantum Shape Dynamics April 10th, 2012 8 / 23