# SU(2) expression

1. Oct 22, 2014

### intervoxel

Please, I'm stuck. How to get the rhs from the lhs?

$X^{\alpha}_{\ \ \alpha^{\ \prime}}X^{\beta}_{\ \ \beta^{\ \prime}}\epsilon^{\alpha^{\ \prime}\beta^{\ \prime}}=det X\epsilon^{\alpha\beta}$

2. Oct 22, 2014

### aleazk

3. Oct 22, 2014

### Meir Achuz

That is one of the definitions of a determinant. The left-hand side is just how you would calculate the value of a determinant. In your case, it is the determinant of a 2 x 2 matrix. Write out a sample case and you will see how it works.