Hamiltonian model of Lorentz invariant particle interactions

Abstract

A model is constructed of interaction in a quantum mechanical system of two spinless particles. The interaction is shown to produce nontrivial scattering. Lorentz symmetry of the model is established by the construction of generators of a unitary representation of the inhomogeneous Lorentz group. The total momentum and angular momentum operators are the same as for a system of two free particles. This ensures familiar transformation properties under space translations and space rotations. The Hamiltonian satisfies the asymptotic condition relative to the Hamiltonian for a system of free particles. The use of the asymptotic condition is shown to be Lorentz invariant. The scattering amplitude is a manifestly invariant function of the particle momentum variables, and can be made to have a variety of analyticity properties by a suitable choice of the arbitrary form factors which occur in the model.