Levi-Civita symbol


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Levi-Civita symbol

[′lā·vē chē·vē′tä ‚sim·bəl]
(mathematics)
A symbol εi,j ,…,s where i, j, …, s are n indices, each running from 1 to n ; the symbol equals zero if any two indices are identical, and 1 or -1 otherwise, depending on whether i, j,…, s form an even or an odd permutation of 1, 2,…, n.
References in periodicals archive ?
Also, Brian Kong and the present author suggested a new area spectrum in [12], boldly claiming that the conventional area spectrum known in loop quantum gravity community could be wrong, if one considers that, for area two-form, one needs to use Levi- Civita tensor instead of Levi-Civita symbol as conventionally used in loop quantum gravity community.
However, Brian Kong and the present author argued in [12] that we arrive at this formula, if we use, in the equation for the area two-form, a Levi-Civita tensor instead of a Levi-Civita symbol as conventionally done in loop quantum gravity community.