Laurent Freidel - Non-string quantum gravity

- Background independence in GR (diffeomorphisms; nonlocal and relational observables)
- Loop QG: quantized Hamiltonian theory, Hilbert space -> spin networks
- Hamiltonian quantization
	- Connection formulation: frame field (distance) + connection (parallel transport)
	- Immirzi parameter: dimensionless coupling in classical action, multiplies torsion; no classical effect except for parity-violating Fermion interaction, but experimental limit is weak
	- Algebra of operators generated by fluxes and holonomies: unique representation (LOST theorem) -> orthonormal basis given by diffeomorphism equivalence class of spin-network functionals
	- (Feynman graphs are spin networks for the Poincaré group)
- Associate geometrical observables to submanifolds of space slices
	- Application: BH entropy propto area by fitting Immirzi parameter
- Dynamics: map to covariant formulation to remove ambiguities
- Spin foams: generated by series of local moves on the initial spin network; each move has quantum amplitude
	- Write gravity as constraint topological BF theory
	- Third quantisation: dictionary between group field and quantum gravity amplitudes
- Problem: coupling to matter of spin-foam models
	- Low energy limits; construct physical observables that can be interpreted classically
	- This is possible in 2+1 gravity -> obtain Ponzano-Regge 1968 model
	- Corresponds to non-commutative field theory
	- Effect of quantum gravity: renormalize gravity; momentum space acquires curvature propto Planck mass; addition of momenta is deformed; minimum length scale accessible to theory; 2+1 gravity restores duality between space and momentum space by curving momentum space
	- Not known if possible to extend this strategy to 4d gravity
- Loop quantum cosmology
	- Minisuperspace quantisation (homogeneous sector); very different than Wheeler-De Witt
	- Discrete cosmological time; remove Big Bang singularity, with deterministic evolution across it (multiple bounce)
	- Inflational at small a(t), semi-classical at low curvatures, yields modified Friedman equation
- Conclusion: LQG yields rich and well defined framework for dealing with quantum gravity in a nonperturbative and background-independent matter; merges with GR and QM
	- Is the theory correct and testable experimentally? We don't know.