Single-Particle Electrodynamics - Assassination Science

A.9.2
Notation for three-space quantities
Three-scalars are denoted by symbols from the standard symbol set. Threevectors
and three-dyads are denoted by boldfacing a symbol from the standard
symbol set.
A three-vector or three-dyad symbol is dereferenced by removing the boldness
of the face and subscripting or superscripting the resulting symbol with
the appropriate index or indices, which take values from the unit-offset threedimensional
enumeration set, i.e., the values 1, 2 and 3. These enumerations
are also given the enumeration names x, y and z respectively.
If a dereferenced three-vector is a non-Lorentz-covariant quantity, then
the choice of whether a subscript or superscript index is used is arbitrary;
the result is deemed to be in all cases the same. If the three-vector is, on the
other hand, the three-vector part of a Lorentz four-vector, then the choice
of subscript or superscript will select the covariant or contravariant version
respectively of the three-vector part of the given four-vector.
Indices for three-vectors are always Latin elements of the standard symbol
set, never Greek, and are preferentially taken from the symbols i, j, k, l, m
and n before any others.
A.9.3
The null three-vector
The null three-vector, (0, 0, 0), is always denoted 0.
A.9.4
The three-gradient operator
The symbol ∇ denotes the three-vector derivative operator, and is defined
to have the explicit components
∇ ≡ (∂ 1 , ∂ 2 , ∂ 3 ) ≡ (∂ x , ∂ y , ∂ z ) .
(A.67)
The symbol ∂, being a special symbol, does not have a standard boldface
359