Editing Conformal symmetry (section)

{{Jargon|date=August 2024}}{{Short description|Extension to the Poincaré group}}

Conformal symmetry is a property of spacetime that ensures angles remain unchanged even when distances are altered. If you stretch, compress, or otherwise distort spacetime, the local angular relationships between lines or curves stay the same. This idea extends the familiar [[Poincaré group]] —which accounts for rotations, translations, and boosts—into the more comprehensive conformal group.

Conformal symmetry encompasses [[special conformal transformation]]s and [[dilation (affine geometry)|dilation]]s. In three spatial plus one time dimensions, conformal symmetry has 15 [[degrees of freedom (physics and chemistry)|degrees of freedom]]: ten for the Poincaré group, four for special conformal transformations, and one for a dilation.

[[Harry Bateman]] and [[Ebenezer Cunningham]] were the first to study the conformal symmetry of [[Maxwell's equations]]. They called a generic expression of conformal symmetry a [[spherical wave transformation]]. [[General relativity]] in two spacetime dimensions also enjoys conformal symmetry.<ref>{{Cite web|title=gravity - What makes General Relativity conformal variant?|url=https://physics.stackexchange.com/q/131305 |website=Physics Stack Exchange|access-date=2020-05-01}}</ref>