Cluster Separability in Relativistic Few Body Problems

TL;DR

This paper discusses the challenge of maintaining cluster separability in relativistic quantum mechanics for few-body systems and proposes a procedure to address this issue.

Contribution

It analyzes the problem of cluster separability in the Bakamjian-Thomas framework and sketches a method to resolve it for systems with more than two particles.

Findings

Identifies the cluster separability problem in relativistic quantum mechanics.

Proposes a procedure to restore cluster separability.

Addresses implications for hadronic physics models.

Abstract

A convenient framework for dealing with hadron structure and hadronic physics in the few-GeV energy range is relativistic quantum mechanics. Unlike relativistic quantum field theory, one deals with a fixed, or at least restricted number of degrees of freedom while maintaining relativistic invariance. For systems of interacting particles this is achieved by means of the, so called, "Bakamjian-Thomas construction", which is a systematic procedure for implementing interaction terms in the generators of the Poincare group such that their algebra is preserved. Doing relativistic quantum mechanics in this way one, however, faces a problem connected with the physical requirement of cluster separability as soon as one has more than two interacting particles. Cluster separability, or sometimes also termed "macroscopic causality", is the property that if a system is subdivided into subsystems which are then separated by a sufficiently large spacelike distance, these subsystems should behave independently. In the present contribution we discuss the problem of cluster separability and sketch the procedure to resolve it.