# Physical significance of Regge symmetry

+ 2 like - 0 dislike
139 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

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.

 Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor)   Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:p$\hbar$ysic$\varnothing$OverflowThen drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). To avoid this verification in future, please log in or register.