Is this the correct use for the Levi-Civita symbol:
\mathcal{E}_ijk
The lowercase "i" looks a bit off to me: $ \mathcal{E}_ijk $
Thanks in advance.
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1 Answer
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If what you want to put in the subscript is not just one symbol you need to contain everything in braces. In your example actually only $i$ is placed correctly as a subscript, which is one reason the thing does not look as you want it to look.
You should write:$\mathcal{E}_{ijk}$ for $\mathcal{E}_{ijk}$
To highlight this note $\sum_{i=1}$ vs $\sum_i=1$ $\sum_{i=1}$ vs $\sum_i=1$
Yet, note that as pointed out by Martin the symbol $\mathcal{E}$ is not commonly used in this context, instead $\varepsilon$ $\varepsilon$ is used, which is smaller than the capital E and thus the proportions relative to the subcript $i$ are different.
\varepsilon_{ijk}when they write, for example: In three dimensions, the Levi-Civita symbol is defined by $$\varepsilon_{ijk} = \begin{cases} +1 & \text{if } (i,j,k) \text{ is } (1,2,3), (2,3,1), \text{ or } (3,1,2), \\ -1 & \text{if } (i,j,k) \text{ is } (3,2,1), (1,3,2), \text{ or } (2,1,3), \\ \;\;\,0 & \text{if } i = j, \text{ or } j = k, \text{ or } k = i \end{cases}$$ $\endgroup$