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Mar 29, 2021 at 11:18 comment added Davide Morgante @fec In this context $\alpha k$ has no specific meaning while $\alpha^k$ is the k-th component of the $\alpha$ vector. The two factors you wrote are identical, it's not important where the $\mu$ index is as long as they are contracted.
Mar 29, 2021 at 8:32 comment added cmmigl I got the symmetric and anti-symmetric part, how do I get $\epsilon^{ijk}(\partial_\mu\pi^i)\pi^j\partial^\mu\alpha^k(x)$ from $\epsilon^{ijk}(\partial^\mu\pi^i)\pi^j\partial_\mu\alpha^k(x)$. Also what does it means to write $\alpha k$ instead of $\alpha^k(x)$
Mar 29, 2021 at 8:00 history answered Davide Morgante CC BY-SA 4.0