  We show that whenever the symmetry group of a field theory commutes with one
or more antiunitary operators $T$, which do not have to but may represent the
reversal of physical time, the number of linearly independent contact two-body
(quartic) terms is determined by the number of tensors that are even, or by the
number of tensors that are odd, under such $T$. The choice depends on the sign
of $T^2$ and on the statistics of the fields. The theorem enables one to
circumvent the usual computation of the Fierz matrix in determining the
independent interaction terms. Some physical examples of current interest in
many-body physics are discussed.
