Fock-tani representation for the quantum theory of reactive collisions

A previously-developed second-quantization representation for nonrelativistic systems of composite bound states and their constituents is extended to any number of composite species. The result is an explicit representation for the kinematics and dynamics of reactive scattering processes (rearrangement collisions). A single Hamiltonian in the new representation simultaneously exhibits the various possible scattering and reaction channels, thus circumventing problems associated with “different Hamiltonians for different channels”. The “unperturbed” Hamiltonian describes the free propagation of all possible bound composites as well as their unbound constituents, while the interaction Hamiltonian describes only true scattering and reaction processes, each term corresponding to a collision process with specified initial and final bound composites and/or unbound constituents. The key to the generalization is a suitable ordering of the composite species and a corresponding ordered-product form of the unitary transformation to the new representation.