In mathematical physics, the conformal symmetry of spacetime is expressed by an extension of the Poincaré group, known as the conformal group. The extension includes special conformal transformations and dilations. In three spatial plus one time dimensions, conformal symmetry has 15 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.[1]
^"gravity - What makes General Relativity conformal variant?". Physics Stack Exchange. Retrieved 2020-05-01.
and 24 Related for: Conformal symmetry information
extension includes special conformal transformations and dilations. In three spatial plus one time dimensions, conformalsymmetry has 15 degrees of freedom:...
A conformal field theory (CFT) is a quantum field theory that is invariant under conformal transformations. In two dimensions, there is an infinite-dimensional...
A conformal anomaly, scale anomaly, trace anomaly or Weyl anomaly is an anomaly, i.e. a quantum phenomenon that breaks the conformalsymmetry of the classical...
conformal geometry is the study of the set of angle-preserving (conformal) transformations on a space. In a real two dimensional space, conformal geometry...
transformations that preserve the conformal geometry of the space. Several specific conformal groups are particularly important: The conformal orthogonal group. If...
half-plane. Fourth, one can use conformalsymmetry to extend harmonic functions to harmonic functions on conformally flat Riemannian manifolds. Perhaps...
invariance or Weyl symmetry. The Weyl symmetry is an important symmetry in conformal field theory. It is, for example, a symmetry of the Polyakov action...
In conformal geometry, a conformal Killing vector field on a manifold of dimension n with (pseudo) Riemannian metric g {\displaystyle g} (also called...
dilatation (also known as dilation). Dilatations can form part of a larger conformalsymmetry. In mathematics, scale invariance usually refers to an invariance...
renormalization group is intimately related to scale invariance and conformal invariance, symmetries in which a system appears the same at all scales (so-called...
coupling where the beta function vanishes – see renormalization group § Conformalsymmetry Temperature reference point, usually defined by a phase change or...
Under conformal transformations, an energy eigenvector with momentum α {\displaystyle \alpha } transforms as a primary field with the conformal dimension...
and mathematical understanding of the theory. His paper "Infinite conformalsymmetry in two-dimensional quantum field theory" written with Alexander Belavin...
(physics), a failure of a symmetry of a theory's classical action Conformal anomaly, a quantum phenomenon that breaks the conformalsymmetry of the classical theory...
Spacetime symmetries are features of spacetime that can be described as exhibiting some form of symmetry. The role of symmetry in physics is important...
Sciences degree (1983). He co-authored the famous BPZ paper "Infinite ConformalSymmetry in Two-Dimensional Quantum Field Theory", with Alexander Polyakov...
readable introduction to the concept of conformal infinity plus examples. Frauendiener, Jörg (2004). "Conformal Infinity". Living Reviews in Relativity...
mirror symmetry. Daniel Friedan, Emil Martinec and Stephen Shenker further developed the covariant quantization of the superstring using conformal field...
L_{n>0}v=0,\quad L_{0}v=hv,} where the number h is called the conformal dimension or conformal weight of v {\displaystyle v} . A highest weight representation...
chiral symmetry and the U(1) baryon number symmetry The following classical symmetries are broken in the QCD Lagrangian: scale, i.e., conformalsymmetry (through...
Massless free scalar bosons are a family of two-dimensional conformal field theories, whose symmetry is described by an abelian affine Lie algebra. Since they...
The conformal bootstrap is a non-perturbative mathematical method to constrain and solve conformal field theories, i.e. models of particle physics or statistical...
Global Information