Quantum constraint dynamics for two spinless particles under vector interaction

Publisher Website
Google Scholar
Abstract
Using Dirac's constraint mechanics we derive two-body Klein-Gordon equations for two spinless particles under mutual vector interaction. We construct generalized mass-shell constraints which incorporate the gauge structure of this interaction for the constituent particles. The resultant direct-interaction formalism does more than just dress static potentials with relativistic two-body kinematics. It includes dynamical recoil effects in the potential characteristic of those that appear in field theories. We demonstrate this classically by showing its canonical equivalence in the slow-motion, weak-potential domain (the semirelativistic approximation) to the Darwin Hamiltonian. We also show this quantum mechanically by demonstrating its equivalence (for weak potentials) to Todorov's homogeneous quasipotential equation (which in turn leads to the standard Breit results for perturbative QED). Not only is our one-body Schrödinger-type equation local and covariant, but also it leads to forms of interaction that make nonperturbative quantum-mechanical sense at short distances. Thus this constraint approach is ideally suited for use in phenomenological applications where a perturbative treatment may be inadequate (with no need for extra smoothing parameters or finite particle size).

This publication has 24 references indexed in Scilit: