  A theorem of Weyl tells us that the Lorentz (and parity) invariant
polynomials in the momenta of $n$ particles are generated by the dot products.
We extend this result to include the action of an arbitrary permutation group
$P \subset S_n$ on the particles, to take account of the
quantum-field-theoretic fact that particles can be indistinguishable. Doing so
provides a convenient set of variables for describing scattering processes
involving identical particles, such as $pp \to jjj$, for which we provide an
explicit set of Lorentz and permutation invariant generators.
