Equation Atlas · Loop quantum gravity
Explore loop quantum gravity through sourced equations, quantum geometry, EPRL boosters and annotated four-simplex diagrams.
Loop quantum gravity · free exploration
Equation Atlas.
Unfold the mathematics one ingredient at a time. Every equation retains its review number, assumptions and source.
0—7
Sets the starting equations. Expand any card independently.Notation & common convention
- j, m
- SU(2) spin and magnetic index.
- i, k
- Intertwiner label and virtual spin; k in (ρ,k) is a Lorentz label.
- ℓ, r
- Auxiliary SU(2) spin and boost rapidity.
- ℓ₀² = 8πγGℏ
- Flux and area unit. γ > 0.
- σ, κ
- Node and induced wedge signs; distinct from wire arrows.
Normalized intertwiners; source-left holonomies; Speziale phases. Toller matrices use the explicit Rühl-to-Speziale conversion.
Shared dataCanonicalCovariant
Formula ↔ wiring
Select a wire for its projected kernel, or a node for its intertwiner.
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