Vector Potential: -1/2 in Coulomb Gauge

[PhysicsGente]

This is not a homework question but I think this is the best place to ask it.

I was reading a book on quantum mechanics and I came across this expression using the Coulomb gauge in a constant magnetic field,

$$\left(\vec{\nabla}\times\vec{A}\right)_{i} = \epsilon_{ijk}\partial_{j}\left(-\frac{1}{2}\epsilon_{kst}x_{s}B_{t}\right)$$

But where is the -1/2 coming from?

 

[TSny]

But where is the -1/2 coming from?

To see it, carry through the exercise of writing out the right hand side for a particular choice of the index $i$.

(Alternately, you could make use of one of the identities of the the Levi-Civita symbol; but, if you are just getting familiar with this notation, I think it's a better exercise to expand the right hand side by thinking about the meaning of the symbols.)