Tensor product structures, entanglement, and particle scattering

Particle systems admit a variety of tensor product structures (TPSs) depending on the complete system of commuting observables chosen for the analysis. Different notions of entanglement are associated with these different TPSs. Global symmetry transformations and dynamical transformations factor into products of local unitary operators with respect to certain TPSs and not with respect to others. Symmetry-invariant and dynamical-invariant TPSs and corresponding measures of entanglement are defined for particle scattering systems.