International
Tables for
Crystallography
Volume D
Physical properties of crystals
Edited by A. Authier

International Tables for Crystallography (2006). Vol. D, ch. 1.1, p. 10

## Section 1.1.3.8.3. Differential operators

A. Authiera*

aInstitut de Minéralogie et de la Physique des Milieux Condensés, Bâtiment 7, 140 rue de Lourmel, 75015 Paris, France
Correspondence e-mail: aauthier@wanadoo.fr

#### 1.1.3.8.3. Differential operators

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If one applies the operator nabla to a scalar ϕ, one obtains This is a covariant vector in reciprocal space.

Now let us form the tensor product of by a vector v of variable components. We then have

The quantities form a tensor of rank 2. If we contract it, we obtain the divergence of v: Taking the vector product, we get The curl is then an axial vector.