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In mathematical physics, inversion transformations are a natural extension of Poincaré transformations to include all conformal, one-to-one transformations on coordinate space-time.[1][2] They are less studied in physics because, unlike the rotations and translations of Poincaré symmetry, an object cannot be physically transformed by the inversion symmetry. Some physical theories are invariant under this symmetry, in these cases it is what is known as a 'hidden symmetry'. Other hidden symmetries of physics include gauge symmetry and general covariance.
- ^ "Chapter 5 Inversion" (PDF). Archived from the original (PDF) on 2021-07-16.
- ^ "THE POINCARE DISK MODEL OF HYPERBOLIC GEOMETRY" (PDF).