Conformal symmetry

In mathematical physics, the conformal symmetry of spacetime is expressed by an extension of the Poincaré group, known as the conformal group; in layman's terms, it refers to the fact that stretching, compressing or otherwise distorting spacetime preserves the angles between lines or curves that exist within spacetime.

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.

In relativistic quantum field theories, the possibility of symmetries is strictly restricted by Coleman–Mandula theorem under physically reasonable assumptions.

Fluctuations[clarification needed] in such systems are conformally invariant at the critical point.

That allows for classification of universality classes of phase transitions in terms of conformal field theories.

Conformal invariance is also present in two-dimensional turbulence at high Reynolds number.

[5] Many theories studied in high-energy physics admit conformal symmetry due to it typically being implied by local scale invariance.

Physicists have found that many lattice models become conformally invariant in the critical limit.

In 2010, the mathematician Stanislav Smirnov was awarded the Fields medal "for the proof of conformal invariance of percolation and the planar Ising model in statistical physics".

[6] In 2020, the mathematician Hugo Duminil-Copin and his collaborators proved that rotational invariance exists at the boundary between phases in many physical systems.