## Permutation Symbol

A three-index object sometimes called the Levi-Civita Symbol defined by

 (1)

The permutation symbol satisfies
 (2) (3) (4) (5)

where is the Kronecker Delta. The symbol can be defined as the Scalar Triple Product of unit vectors in a right-handed coordinate system,
 (6)

The symbol can also be interpreted as a Tensor, in which case it is called the Permutation Tensor.

References

Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 132-133, 1985.