Background-independent quantisation programme for general relativity in which the gravitational field is described by SU(2) holonomies along loops (spin-network states). Discrete spectra of area and volume operators, no unified matter…
loop-quantum-gravity
Ashtekar variables
Reformulation of GR in terms of a densitised SU(2) triad Ẽ^a_i (electric) and a connection A^i_a (magnetic). Converts the Hamiltonian…
Wilson loops in gravity
Holonomy h_γ[A] = P exp(∫_γ A) of the Ashtekar connection along a loop γ. Gauge-invariant class functions of holonomies span the…
Spin network
Graph with edges labelled by SU(2) representations (half-integer j) and vertices by SU(2) intertwiners. Orthonormal basis of the…
Area operator spectrum
Quantised area operator acting on a spin network has discrete spectrum A = 8πγℓ_P² Σ_e √j_e(j_e+1), with Barbero–Immirzi parameter γ.…
Volume operator (LQG)
Analogous discretisation of the 3-volume on spin networks; eigenvalues concentrated on vertices of valence ≥4. The Hamiltonian constraint…
Spin foam (path-integral)
Sum over 2-complexes (histories of spin networks) with amplitudes derived from BF theory + simplicity constraints (EPRL/FK models).…
Barbero–Immirzi parameter
Free dimensionless parameter γ in the Ashtekar connection A^i_a = Γ^i_a + γK^i_a. Fixes the scale of the area and volume spectra; matched…
Loop quantum cosmology
Symmetry-reduced LQG applied to Friedmann–Robertson–Walker universes. Replaces the classical Big-Bang singularity with a quantum 'big…
SU(2) spin-network evaluation (Penrose–Reshetikhin–Turaev, LQG)
Loop-quantum-gravity application of L0 monoidal-category theory. A spin network Γ is a trivalent graph whose edges carry half-integer…
Ponzano–Regge state-sum model (2+1 quantum gravity, LQG)
Loop-quantum-gravity application of L0 2-category and simplicial-set theory. Ponzano and Regge 1968 proposed the first state-sum model of…