I'm reading a paper which says that since $\alpha_k$ is real $$|-\alpha_k> = |(-\alpha_k,0)^T> = |(0, -\alpha_k)^T> $$
I'm confused about the notation and don't understand what the zeroes inside the bracket mean. This is mentioned in context of the initial conditions for a time-dependent RG analysis, so does the $0$ represent $t = 0$ ? If so, why does the statement follow from $\alpha_k$ being real?
$|\alpha_k>$ is the usual coherent state.