The N-Quantum Approximation and Bound States in Motion

TL;DR

This paper introduces the N-Quantum approximation as an alternative to the Bethe-Salpeter equation for analyzing relativistic bound states in motion, providing a new method that explicitly demonstrates Lorentz contraction.

Contribution

The paper develops a new bound state equation using the N-Quantum approximation, simplifying the process and confirming Lorentz contraction effects in relativistic bound states.

Findings

Derived a relativistic bound state equation showing Lorentz contraction

Validated the NQA method against Bethe-Salpeter results

Presented diagram interpretation rules for the NQA

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.