Symmetry conforms

In Theoretical physics, the symmetry conforms indicates the symmetry under change of scale, one also says under dilation, like the transformations in conformity special . Its combination with the Groupe of Poincaré gives the group of symmetry conforms or more simply, group conforms .

Here an example of representation of the group in conformity in the Space time, or more precisely of sound Algebra of Dregs

\begin{matrix}
Naked M_ {\ driven \} & \ equiv &-i (x_ \ driven \ partial_ \ nu-x_ \ naked \ partial_ \ driven) \ \
P_ \ mu& \ equiv & - I \ partial_ \ driven \ \
D& \ equiv &-x_ \ driven \ partial^ \ driven \ \
K_ \ mu& \ equiv & {I \ over2} (x^2 \ partial_ \ mu-2x_ \ driven x_ \ naked \ partial^ \ naked) \ \
\ end {matrix} \,

where the $M_ {\ driven \ naked} \,$ are the generators associated with the Groupe with Lorentz, the $P_ \ driven \,$ generate the translations of space-temsps (eigenvalues of the latter correspondent to the Quadrivecteur impulse-energy), $D \,$ generates the transformation by Dilatation and finally the $K_ \ driven \,$ generate the transformations in conformity special.

The relations of Commutation between these generators, additional with those of the group of Poincaré are

=0 \,

=-K_ \ driven \,

$=P_ \ driven \,$ , $=0 \,$

$= \ eta_ {\ driven \ naked} naked D-iM {\ driven \} \,$

In addition, $D \,$ is a Scalaire of Lorentz and $K_ \ driven \,$ is a vector covariant under the Transformations of Lorentz.

If one considers a two-dimensional space time then the transformations of the group conforms are called transformations in conformity and in this very particular case the group in conformity becomes of infinite Dimension.

Uses in physics

One sees the appearance of invariance in conformity in the phenomena of Turbulence in two dimensions with large a Reynolds number.

There exists a conjecture affirming that all Quantum theory of the fields which is in more invariant of scale admits the group in conformity complete like groups total symmetry. A particular application of this conjecture is given in the study of the critical phenomena (Transition from phase of the second order) in systems having of the local interactions. The fluctuations of such systems are invariant in conformity with the not criticizes and can thus be described by a Théorie in conformity of the fields.

Largest total Groupe of symmetry possible of a supersymmetric Quantum theory of the fields not having interactions is a direct Produit of the group in conformity with a internal Groupe of symmetry.

In High-energy physics several theories have symmetry conforms

the Théorie of Yang-Millets supersymmetric N=4.
the theory of the fields living on the Surface of universe of the cords within the framework of the Theory of the cords.

See too

Algebra superconforme
Theorem of Coleman-Mandula
Invariance of scale
Group of renormalization

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