SU(2): Get RHS from LHS of Expression

[intervoxel]

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

<br /> X^{\alpha}_{\ \ \alpha^{\ \prime}}X^{\beta}_{\ \ \beta^{\ \prime}}\epsilon^{\alpha^{\ \prime}\beta^{\ \prime}}=det X\epsilon^{\alpha\beta}<br />

 

[aleazk]

http://en.wikipedia.org/wiki/Levi-Civita_symbol#Applications_and_examples

 

[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.