The N-Quantum Approximation and Bound States in Motion

Abstract

We use an alternative method to the Bethe-Salpeter equation, the N-Quantum approximation (NQA), for studying bound states in motion. We use this method to find a relativistic equation for weakly bound states of two constituents with different masses. We present rules for interpreting simple diagrams associated with the NQA. We can use these rules to construct the bound state equations directly, avoiding some of the complications of the process. The final result is a bound state equation that shows Lorentz contraction in the direction of motion explicitly. This result matches that of [3] found using the Bethe-Salpeter equation. We briefly discuss some other applications of the NQA in studying the effects of motion on bound states.