Myth of scattering in finite volume

Understand

In this notes, we illustrate why the infinite volume scattering amplitude is in fact dispensable when it comes to formulating few-body quantization condition in finite volume.

• Only subprocess interactions or interactions associated subprocess amplitudes are essential and fundamental ingredients of quantization conditions.
• After these ingredients are determined, infinite volume scattering amplitude can be computed separately.
• The underlying reasons are rooted in facts that (1) the final physical process is generated by all subprocess or interactions among particles; (2) the ultimate goal of quantization condition in finite volume is to find stationary solutions of few-body system.