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  Physical significance of Regge symmetry

+ 2 like - 0 dislike
659 views

In the representation theory of $SU_2$ a big role is played by so-called $6-j$symbols

$$\begin{bmatrix}
a & b & c\\
d & e & f\\
\end{bmatrix}.$$

There definition can be found here.

Among there  symmetries the most mysterious is a famous Regge symmetry:

$$
\begin{bmatrix}
a & b & c\\
d & e & f\\
\end{bmatrix}=
\begin{bmatrix}
a & s-b & s-c\\
d & s-e & s-f\\
\end{bmatrix},
$$
where $s=\frac{b+c+e+f}{2}.$

What is the physical significance of this symmetry?  Are there any currently known applications of it?

asked Aug 31, 2018 in Theoretical Physics by rudenkodaniil (10 points) [ no revision ]

It would be inefficient to paraphrase Philip Boalch in REGGE AND OKAMOTO SYMMETRIES which gives geometric and algebraic interpretations in chapter 2. Background. ( It is not a matrix, the Wignet encoding uses {} ). It is easy to check the symmetries with Mathematica and many other libraries or by the analyse of the Wigner formulation.

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