Diagram Lab · Loop quantum gravity

Explore loop quantum gravity through sourced equations, quantum geometry, EPRL boosters and annotated four-simplex diagrams.

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Loop quantum gravity · exact topology

Diagram Lab.

The five tetrahedra and ten wires of a four-simplex boundary. The port ordering follows the supplied TikZ macro; crossings carry no extra vertices.

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Inspect a wire or tetrahedron

Causal assignments

Show induced causal signs

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All ten spin labels and wire types

Gluing a shared tetrahedron

The two boundary state spaces are dualized. Matching four external spins is necessary; the shared intertwiner is summed in an orthonormal basis. Reversing a port pairing can require a recoupling matrix.

Port map1→1, 2→2, 3→3, 4→41→4, 2→3, 3→2, 4→1

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