  Low energy weak interactions calculations with fermions frequently involve a
superposition of quartic products of Dirac spinors, in which the order of the
spinors is not the same in all the contributing terms. A common trick that is
used to bring them to a uniform ordering is the Fierz transformation. We show
that the standard Fierz rearrangement formula quoted in textbooks is one
element of a class of transformations of a quartic product amplitude, under
which the spinors are rearranged with different orderings and, in the general
case, some or all of the spinors are transformed to their Lorentz-invariant
complex conjugate form. We give a pedagogical derivation of the explicit forms
of all such transformation matrices. In addition to the usual Lorentz scalar
quartic products, we consider pseudoscalar ones as well. Such manipulations and
formulas are useful, in particular, when some of the fermions involved are
Majorana particles.
