We define shift operators
and
which apply to expressions
where
and
are constant vectors. Let
be the operator for differentiation. It can be checked that
Define the shift operators by
We see that
applied to
increments the
th upper index of
. Similarly, define the shift operator
by
It can be seen that
applied to
decrements the
th lower index of
. Visibly,
where
are unit vectors. We need
and
for
and
to be defined.
