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⊂Sn 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→jjj, for which we provide an explicit set of Lorentz and permutation invariant generators.