Spacetime Symmetry Groups & Toy Models

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Abstractions about symmetry groups and simplified models in relativistic physics, covering spacetime symmetry groups (Einstein Group, Galilean Group, Wigner D-Matrix), toy models of gravity (CGHS Model, Causal Dynamical Triangulation), and geometric constructs like the Spherical 3-Manifold.

6 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

• Causal Dynamical Triangulation — A nonperturbative lattice-gravity construction that sums Regge-weighted, causally admissible piecewise-flat spacetime histories and searches their phase structure for a continuum quantum geometry.
• CGHS model — The Callan–Giddings–Harvey–Strominger (CGHS) model is a toy model of general relativity in 1 spatial and 1 time dimension.
• Einstein Group — Note that the Einstein group approaches—but never reaches—the Poincare group as the flat spacetime (special relativity limit) is approached.
• Galilean Group — Without the translations in space and time the group is the homogeneous Galilean group.
• Spherical 3-manifold — In mathematics, a spherical 3-manifold M is a 3-manifold of the form.
• Wigner D-Matrix — The spin-j unitary matrix of an SO(3) or SU(2) rotation in the spherical angular-momentum basis, with Euler-angle factorization exposing its reduced small-d functions.