# Needed small explanation of the notation in this paper [duplicate]

In equation (36) of this, the second line ($\omega^{+ij} =\dots$), there is a term $\partial_{[i}\bar\lambda\delta_{j\,]k}$ that I didn't understand. What does this notation mean?

• – Christoph Nov 22 '14 at 18:49
• As Christoph said, this is antisymmetric notation, but be cautious. Sometimes people don't use $n!$ multiplication in front of it. So, up to $n!$ or $1/n!$, $A_{[i}B_{j]}=A_iB_j-A_jB_i$ – MEDVIS Nov 22 '14 at 18:55
• – Qmechanic Nov 22 '14 at 18:56
• @Fluctuations: $\delta_{jk}$ is the Kronecker-delta (a rank-2 tensor), but you only anti-symmetrize over one of its indices, leaving $k$ fixed – Christoph Nov 22 '14 at 19:14
• @Fluctuations: Right (modulo a factor of $1/2$ depending on the chosen convention) – Christoph Nov 22 '14 at 19:21